Invariants.lookup_preserves_critbit: law of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/invariants.bend as Invariants
Lines 125-132 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/invariants.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/invariants.bend&start_line=125&end_line=132

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/native_map.bend as Native

# Lookup preserves even the strengthened discriminator/prefix predicate. The
# general storage preservation law does not need an assumed valid input tree.
law lookup_preserves_critbit:
  for -V: Data
  for +d: V
  for +m: Map<&2, V>
  for +key: String
  {critbit(V, Native.lookup_map(V, Map.get(V, d, m, key))) == critbit(V, m) : Bool}

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=String
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/invariants.bend&name=critbit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/native_map.bend&name=lookup_map
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/native_map.bend&name=lookup_preserves_map