proofs/containers/balanced_search_tree/dfix.bend checks

raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/balanced_search_tree/dfix.bend as Dfix

20 imports

import Base
import ../../lib/logic.bend as L
import ../../lib/nat.bend as N
import ../../lib/order.bend as O
import ../../../spec/lib/common.bend as SC
import ../../../src/containers/balanced_search_tree.bend as M
import ./state.bend as ST
import ./mirror.bend as MI
import ./tree.bend as TR
import ./ends.bend as EN
import ./path.bend as P
import ./plug.bend as PG
import ./setters.bend as SE
import ./rotm.bend as RM
import ./rotp.bend as RP
import ./nbr.bend as NB
import ./dj.bend as DJ
import ./spath.bend as SP
import ./fix.bend as FX
import ../../lib/nat_list.bend as NL

Templates

template dstop source · line 40 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+h1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0n, nl) == True{} : Bool} -> @+h2:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t) : Nat} -> @+h3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0n, 0n, False{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

a linked tree of the ids and a step that stopped: the loop blackens the root

template dfin source · line 48 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.black_root(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

the path invariant gives the whole tree

template dup_l source · line 55 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.set_red(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), True{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_parent(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p)), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

both nephews black: the sibling red, then on from the parent

template dborrow_l source · line 63 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_borrow_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dfar_l source · line 84 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+y:Nat -> @+ya:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+yb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}, sb}}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}, sb}})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_far_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), False{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dfar0_l source · line 105 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hnr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sa))) == True{} : Bool} -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_far_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), False{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

a red near nephew is a node

template dkids_l source · line 114 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+nr:Bool -> @+hnr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sa))) == nr : Bool} -> @+fr:Bool -> @+hfr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sb))) == fr : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_children_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), nr, fr)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

the nephews' colours

template dsib2_l source · line 127 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_children_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_left(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_right(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

the sibling's children

template dsib_l source · line 138 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_sibling_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

reading the parent and the sibling

template dred_l source · line 146 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+b:Bool -> @+hb:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))) == b : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_red_sibling_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), b)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dside_l source · line 165 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, True{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side_left(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

x on the left: read the sibling

template dup_r source · line 172 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.set_red(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), True{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_parent(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p)), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dborrow_r source · line 179 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_borrow_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dfar_r source · line 198 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+y:Nat -> @+ya:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+yb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}}, t}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}}, t})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{y, ya, yb}}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_far_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), False{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dfar0_r source · line 218 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+hnr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sb))) == True{} : Bool} -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c1), nl) == True{} : Bool} -> @+hok:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c1, p, nl) == True{} : Bool} -> @+hnd:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1)))) == True{} : Bool} -> @+hroot:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t})) : Nat} -> @+hids:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}, t}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c1))) == i0 : List<&2, Nat>} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_far_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), False{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dkids_r source · line 226 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+w:Nat -> @+sa:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+sb:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{w, sa, sb}} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+nr:Bool -> @+hnr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sb))) == nr : Bool} -> @+fr:Bool -> @+hfr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(sa))) == fr : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_children_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, w, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, w), nr, fr)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dsib2_r source · line 238 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_children_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_right(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_left(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dsib_r source · line 248 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_sibling_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dred_r source · line 254 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+b:Bool -> @+hb:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))) == b : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_red_sibling_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s), b)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dside_r source · line 272 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side_right(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dsame source · line 281 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+he:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s)) == True{} : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), True{})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

x and its sibling with the same id: both empty, so x may as well be on the left

template dsd source · line 300 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, False{}, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+e:Bool -> @+he:{Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s)) == e : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), e)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

x on the right: its id against the sibling's

template dlft source · line 308 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c1:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+p:Nat -> @+lft:Bool -> @+s:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{p, lft, s} <> c1, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), p, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, p), Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, lft, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(s))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

the side x hangs on

template dside source · line 318 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+hb:{Bool.or(Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), root), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t)))) == False{} : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_side(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c)), Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_left(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c)))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

not stopping: x is not the root, so it has a parent

template dstop2 source · line 329 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> @+b:Bool -> @+hb:{Bool.or(Nat.is_eq(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), root), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_red(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t)))) == b : Bool} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_stop(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c)), b)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

stopping: x goes black, and the loop blackens the root

template dstep source · line 337 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @kont:(@+kr_:Nat -> @+kn_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+kc_:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+kt_:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+ki1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, kt_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), kn_) == True{} : Bool} -> @+ki2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, kc_, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), kn_) == True{} : Bool} -> @+ki3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_)))) == True{} : Bool} -> @+ki4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(kc_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(kc_))) == i0 : List<&2, Nat>} -> @+ki5:{kr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(kc_, kt_)) : Nat} -> @+kh4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, kn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+kh5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, kn_, pl) == True{} : Bool} -> @+kh6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, kn_, fx) == True{} : Bool} -> @+kh7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, kn_) == l0 : Nat} -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, kr_, lo, hi, free, l, d, kn_, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(kt_), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(kc_), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>) -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, 1n+gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), True{}})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

template dloop source · line 342 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+n:Nat -> @+lo:Nat -> @+hi:Nat -> @+free:Nat -> @+l:Nat -> @+d:Nat -> @+pl:List<&2, Maybe<&2, V>> -> @+tg:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+fl:List<&2, Nat> -> @+fx:List<&2, Nat> -> @+i0:List<&2, Nat> -> @+e0:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>> -> @+l0:Nat -> @+gf:Nat -> @+root:Nat -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+i1:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+i2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.ctxok(K, c, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), nl) == True{} : Bool} -> @+i3:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/nat_list.nodupn(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)))) == True{} : Bool} -> @+i4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == i0 : List<&2, Nat>} -> @+i5:{root == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/plug.plug(c, t)) : Nat} -> @+h4:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, nl, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+h5:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, nl, pl) == True{} : Bool} -> @+h6:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, nl, fx) == True{} : Bool} -> @+h7:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, nl) == l0 : Nat} -> @+b:Bool -> Sigma<&1, &1, Nat, fr_ => Sigma<&1, &1, List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>>, fn_ => Sigma<&1, &1, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr, ft_ => Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/mirror.delete_fix_loop(K, V, cmp, gf, (0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, root, lo, hi, free, l, d, nl, pl, tg, fl}, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.DF{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(t), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), b})) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.SH{n, fr_, lo, hi, free, l, d, fn_, pl, tg, fl} : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Sh<K, V>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, ft_, 0n, fn_) == True{} : Bool}, Pair({fr_ == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(ft_) : Nat}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(ft_) == i0 : List<&2, Nat>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.root_black(K, ft_, fn_) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, i0, fn_, pl) == e0 : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, i0, fn_, pl) == True{} : Bool}, Pair({0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fll(K, fn_, fx) == True{} : Bool}, {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>, fn_) == l0 : Nat}))))))))>>>

from the position x under its parent, the loop ends with the ghost tree's properties, whatever its fuel and flag