ProofBase.le_ne: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_base.bend as ProofBase
Lines 540-546 of minebender-game@1.0.0.0/proof_base.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_base.bend&start_line=540&end_line=546

import Base

# a <= b and a != b give a + 1 <= b.
law le_ne:
  for +a: Nat
  for +b: Nat
  for le: {Nat.is_le(a, b) == True{} : Bool}
  for ne: {Nat.is_eq(a, b) == False{} : Bool}
  {Nat.is_le(1n+a, b) == True{} : 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=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=le_zero_l
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=true_ne_false