ProofAppend.slice_cons: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_append.bend as ProofAppend
Lines 92-99 of lawful-bytes@0.1.1.0/proof_append.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&start_line=92&end_line=99

import Base
import lawful-bytes@0.1.1.0/defs.bend as D

# A slice of 1 + k from i starts with element i.
law slice_cons:
  for +xs: List<&2, U32>
  for +i: Nat
  for +k: Nat
  for +x: U32
  for +h: {List.get(&2, U32, xs, i) == Some{x} : Maybe<&2, U32>}
  {D.slice(xs, i, 1n+k) == x <> D.slice(xs, Nat.add(i, 1n), k) : List<&2, U32>}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=drop_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=none_some
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=some_inj