PROOF.un.le_not_lt: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 260-269 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=260&end_line=269

import Base

def un.le_not_lt(b: Nat, a: Nat, h: {Nat.is_le(b, a) == True{} : Bool}) -> {Nat.is_lt(a, b) == False{} : Bool}:
  match b a:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      Empty.absurd({Nat.is_lt(0n, 1n+p) == False{} : Bool}, un.ft(h))
    case 1n+p 1n+q:
      un.le_not_lt(p, q, h)

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.ft