LAWS.to_nat_inc_lt: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/LAWS.bend as LAWS
Lines 137-142 of lawful-words@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/LAWS.bend&start_line=137&end_line=142

import Base

# A counter below some word steps up by exactly one.
law to_nat_inc_lt:
  for a: U32
  for b: U32
  for h: {U32.is_lt(a, b) == True{} : Bool}
  {U32.to_nat(U32.inc(a)) == Nat.add(U32.to_nat(a), 1n) : Nat}

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=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=Base/base.bend&name=U32.inc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_inc_lt