PROOF.un.nlt_le: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1514-1524 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=1514&end_line=1524

import Base

# not x < y: y <= x
def un.nlt_le(x: Nat, y: Nat, e: {Nat.is_lt(x, y) == False{} : Bool}) -> {Nat.is_le(y, x) == True{} : Bool}:
  match x y:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      Empty.absurd({Nat.is_le(1n+q, 0n) == True{} : Bool}, un.tf(e))
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      un.nlt_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-osdev-u32@0.1.0.0/PROOF.bend&name=un.tf