proofs/containers/balanced_search_tree/navs.bend checks

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

15 imports

import Base
import ../../lib/logic.bend as L
import ../../lib/order.bend as O
import ../../lib/list.bend as LL
import ../../../spec/lib/common.bend as SC
import ../../../spec/containers/balanced_search_tree/main.bend as S
import ../../../src/containers/balanced_search_tree.bend as M
import ./state.bend as ST
import ./ord.bend as OR
import ./find.bend as FI
import ./ends.bend as EN
import ./tree.bend as TR
import ./path.bend as P
import ./nav.bend as NV
import ./navl.bend as NL

Definitions

def wh_node source · line 133 · raw

@+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> {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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), i <> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) : List<&2, Nat>}

the ids split around a node: before and its left ids, the node, its right ids and after

Templates

template oks_l source · line 23 · raw

@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+xs:List<&2, Nat> -> @+ys:List<&2, Nat> -> @+h:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, xs, ys), nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, xs, nl, pl) == True{} : Bool}

template oks_r source · line 30 · raw

@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+xs:List<&2, Nat> -> @+ys:List<&2, Nat> -> @+h:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, xs, ys), nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, ys, nl, pl) == True{} : Bool}

template nav_te source · line 39 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+hk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TE{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl) == True{} : Bool} -> @+hb:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.ltall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), nl, pl)) == True{} : Bool} -> @+ha:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.gtall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TE{}, c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TE{}, c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TE{}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}

template geq source · line 58 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+key:K -> @+v:V -> @+hE:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, i)) == Some{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v}} : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+hc:{cmp(k, key) == EQ{} : Cmp} -> @+ho:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ordered(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v} <> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl))) == True{} : Bool} -> @+hkx:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl) == True{} : Bool} -> @+hky:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v} <> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl))) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}

template gcase source · line 99 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+key:K -> @+v:V -> @+hE:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, i)) == Some{0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v}} : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+hW:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v} <> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl)) : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+ho:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ordered(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry{key, v} <> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl))) == True{} : Bool} -> @+hkx:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl) == True{} : Bool} -> @+hky:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl) == True{} : Bool} -> @+eqL:{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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c))) : List<&2, Nat>} -> @+eqR:{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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c))) : List<&2, Nat>} -> @kl:(@+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.gtall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}) -> @kr:(@+hr2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.ltall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}) -> @+cc:Cmp -> @+hc:{cmp(k, key) == cc : Cmp} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/tree.pk3(Nat, cc, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/tree.pk3(Nat, cc, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}

template gnode source · line 119 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+x:0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K> -> @+m:Maybe<&2, V> -> @+hx:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.is_node(K, x, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(l), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rid(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c)) == True{} : Bool} -> @+hm:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.some2(V, m) == True{} : Bool} -> @+hxi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i) == x : 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>} -> @+hEg:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, i)) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, x, m) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+hW0:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.cons_m(0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, i)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl))) : List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>} -> @+ho:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ordered(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl)) == True{} : Bool} -> @+hkx:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl) == True{} : Bool} -> @+hky:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl) == True{} : Bool} -> @+eqL:{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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c))) : List<&2, Nat>} -> @+eqR:{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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c))) : List<&2, Nat>} -> @kl:(@+hl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.gtall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}) -> @kr:(@+hr2:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.ltall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}) -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}, c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}, c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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(0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.TN{i, l, r}), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}

template gspec source · line 138 · raw

@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @-o:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/order.Order(K, cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+t:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+hr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.rep(K, t, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.top(c), nl) == True{} : Bool} -> @+hp:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pay(V, t, pl) == True{} : Bool} -> @+ho:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ordered(K, V, cmp, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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))), nl, pl)) == True{} : Bool} -> @+hk:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 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))), nl, pl) == True{} : Bool} -> @+hb:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.ltall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), nl, pl)) == True{} : Bool} -> @+ha:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ord.gtall(K, V, cmp, k, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c), nl, pl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, t, c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, t, c, nl, k, h, incl))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.nav(K, V, cmp, k, h, incl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ents(K, V, 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))), nl, pl)) : Maybe<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Entry<K, V>>}

the entry at the ghost navigation's id is the specification's answer