Nat.not_lt_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 163-171 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=163&end_line=171

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

# is_lt(a, b) == False gives b <= a.
def not_lt_le(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == False{} : Bool}) -> {Nat.is_le(b, a) == True{} : Bool}:
  match a b:
    case _ 0n:
      zero_le(a)
    case 0n 1n+q:
      Empty.absurd({Nat.is_le(1n+q, 0n) == True{} : Bool}, L.true_false(e))
    case 1n+p 1n+q:
      not_lt_le(p, q, e)

Uses (7):
  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/logic.bend&name=true_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=zero_le