proofs/containers/hash_table/state.bend checks

raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/hash_table/state.bend as State

14 imports

import Base
import ../../lib/logic.bend as L
import ../../lib/nat.bend as N
import ../../lib/array.bend as AR
import ../../../spec/lib/common.bend as SC
import ../../../spec/containers/hash_table.bend as S
import ../../lib/u32div.bend as UD
import ../../../src/containers/hash_table.bend as H
import ./table.bend as TB
import ./buckets.bend as B
import ./cyc.bend as CY
import ./inv.bend as IV
import ../../lib/nat_list.bend as NL
import ../../lib/words32.bend as W32

Types

type Sh source · line 20 · raw

@-V:Data -> Data

HS

@-V:Data -> @n:U32 -> @k:Nat -> @td:U32 -> @fresh:U32 -> @sz:U32 -> @sd:Nat -> @sdU:U32 -> @free:U32 -> @tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @ksT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<String> -> @vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Sh<V>

Definitions

def noslot source · line 92 · raw

@+bs:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk> -> @+s:Nat -> @+m:Nat -> Bool

no full bucket among the first m uses slot s

def fl_ok source · line 101 · raw

@+bs:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk> -> @+nb:Nat -> @+nxl:List<&2, U32> -> @+cnt:Nat -> @+f:U32 -> @+fr:Nat -> @+seen:List<&2, Nat> -> Bool

the free list from link f has exactly cnt links: each slot on it is below fresh, used by no bucket and not repeated, and the list ends after them

Templates

template real source · line 23 · raw

@-V:Data -> @sh:Sh<V> -> 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/hash_table.HashMap<&2, V>

template some_b source · line 30 · raw

@-V:Data -> @m:Maybe<&2, V> -> Bool

template lvs source · line 37 · raw

@-V:Data -> @vsl:List<&2, Maybe<&2, V>> -> List<&2, Bool>

template nthm source · line 44 · raw

@-V:Data -> @vsl:List<&2, Maybe<&2, V>> -> @+i:Nat -> Maybe<&2, V>

template ent_m source · line 53 · raw

@-V:Data -> @+k:String -> @m:Maybe<&2, V> -> List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.Entry<V>>

template ent source · line 61 · raw

@-V:Data -> @b:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk -> @+vsl:List<&2, Maybe<&2, V>> -> List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.Entry<V>>

the entry of a bucket

template absm source · line 69 · raw

@-V:Data -> @+bs:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk> -> @+vsl:List<&2, Maybe<&2, V>> -> @+m:Nat -> @+j:Nat -> List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.Entry<V>>

the entries of buckets j .. j + m - 1, in bucket order

template bsof source · line 76 · raw

@-V:Data -> @sh:Sh<V> -> List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.Bk>

template model source · line 81 · raw

@-V:Data -> @sh:Sh<V> -> List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/hash_table.Entry<V>>

template ck source · line 108 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template csd source · line 111 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cpt source · line 114 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cpk source · line 117 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cpv source · line 120 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cpn source · line 123 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template ctd source · line 126 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template csz source · line 129 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template csdu source · line 132 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cwell source · line 135 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cclus source · line 138 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cuniq source · line 141 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cn source · line 144 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cload source · line 147 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template clive source · line 150 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cfresh source · line 153 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template cfree source · line 156 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template csdk source · line 159 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr16 source · line 162 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr15 source · line 165 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr14 source · line 168 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr13 source · line 171 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr12 source · line 174 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr11 source · line 177 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr10 source · line 180 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr9 source · line 183 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr8 source · line 186 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr7 source · line 189 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr6 source · line 192 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr5 source · line 195 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr4 source · line 198 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr3 source · line 201 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr2 source · line 204 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template gr1 source · line 207 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template goodF source · line 210 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> Bool

template good source · line 213 · raw

@-V:Data -> @sh:Sh<V> -> Bool

template gp1 source · line 218 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr1(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp2 source · line 221 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr2(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp3 source · line 224 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr3(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp4 source · line 227 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr4(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp5 source · line 230 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr5(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp6 source · line 233 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr6(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp7 source · line 236 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr7(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp8 source · line 239 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr8(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp9 source · line 242 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr9(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp10 source · line 245 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr10(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp11 source · line 248 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr11(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp12 source · line 251 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr12(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp13 source · line 254 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr13(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp14 source · line 257 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr14(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp15 source · line 260 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr15(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp16 source · line 263 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {gr16(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template gp17 source · line 266 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {csdk(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_ck source · line 269 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {ck(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_csd source · line 272 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {csd(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cpt source · line 275 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cpt(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cpk source · line 278 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cpk(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cpv source · line 281 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cpv(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cpn source · line 284 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cpn(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_ctd source · line 287 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {ctd(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_csz source · line 290 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {csz(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_csdu source · line 293 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {csdu(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cwell source · line 296 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cwell(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cclus source · line 299 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cclus(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cuniq source · line 302 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cuniq(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cn source · line 305 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cn(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cload source · line 308 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cload(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_clive source · line 311 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {clive(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cfresh source · line 314 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cfresh(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_cfree source · line 317 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {cfree(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template g_csdk source · line 320 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+g:{goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {csdk(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

template good_intro source · line 324 · raw

@-V:Data -> @+n:U32 -> @+k:Nat -> @+td:U32 -> @+fresh:U32 -> @+sz:U32 -> @+sd:Nat -> @+sdU:U32 -> @+free:U32 -> @+tabT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+kl:List<&2, String> -> @+pk:Bool -> @+vsT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<Maybe<&2, V>> -> @+nxT:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/lib/array.Tree<U32> -> @+h_ck:{ck(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_csd:{csd(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cpt:{cpt(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cpk:{cpk(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cpv:{cpv(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cpn:{cpn(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_ctd:{ctd(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_csz:{csz(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_csdu:{csdu(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cwell:{cwell(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cclus:{cclus(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cuniq:{cuniq(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cn:{cn(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cload:{cload(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_clive:{clive(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cfresh:{cfresh(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_cfree:{cfree(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> @+h_csdk:{csdk(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool} -> {goodF(V, n, k, td, fresh, sz, sd, sdU, free, tabT, kl, pk, vsT, nxT) == True{} : Bool}

the invariant from its components

template lvs_nth source · line 329 · raw

@-V:Data -> @+vsl:List<&2, Maybe<&2, V>> -> @+i:Nat -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/hash_table/buckets.nthb(lvs(V, vsl), i) == some_b(V, nthm(V, vsl, i)) : Bool}

template nthm_some source · line 338 · raw

@-V:Data -> @+vsl:List<&2, Maybe<&2, V>> -> @+i:Nat -> @+h:{Nat.is_lt(i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.length(Maybe<&2, V>, vsl)) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.nth(Maybe<&2, V>, vsl, i) == Some{nthm(V, vsl, i)} : Maybe<&2, Maybe<&2, V>>}