ProofFind.step_lt: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_find.bend as ProofFind
Lines 201-209 of lawful-bytes@0.1.1.0/proof_find.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_find.bend&start_line=201&end_line=209

import Base

# With j + 1 + k = to <= len, byte j is in range.
law step_lt:
  for +len: U32
  for +j: U32
  for +to: U32
  for +k: Nat
  for +hn: {Nat.add(U32.to_nat(j), 1n+k) == U32.to_nat(to) : Nat}
  for +hto: {Nat.is_le(U32.to_nat(to), U32.to_nat(len)) == True{} : Bool}
  {Nat.is_lt(U32.to_nat(j), U32.to_nat(len)) == True{} : Bool}

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_find.bend&name=lt_add_succ
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans