Nat.lt_not_le: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 182-189 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&start_line=182&end_line=189

import Base

def lt_not_le(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_le(b, a) == False{} : Bool}:
  match a b:
    case _ 0n:
      Empty.absurd({Nat.is_le(0n, a) == False{} : Bool}, lt_zero_absurd(a, e))
    case 0n 1n+q:
      {==}
    case 1n+p 1n+q:
      lt_not_le(p, q, e)

Uses (6):
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd