MapInsert.splice_same: law of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend as MapInsert
Lines 109-116 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend&start_line=109&end_line=116

import Base

law splice_same:
  for -V: Data
  for d: V
  for x: V
  for rest: Map<&2, V>
  for +p: Nat
  for +key: String
  {lookup(V, d, Map.ins.splice(&2, V, p, key, x, rest), key) == x : V}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map.bit
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map.ins.splice
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Map.ins.splice.bit
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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/map_insert.bend&name=lookup
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend&name=route_bit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend&name=route_shape
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/map_insert.bend&name=splice_same_bit