PROOF.un.lt_succ_r: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 171-178 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=171&end_line=178

import Base

def un.lt_succ_r(x: Nat, y: Nat, h: {Nat.is_lt(x, y) == True{} : Bool}) -> {Nat.is_lt(x, 1n+y) == True{} : Bool}:
  match x y:
    case 0n _:
      {==}
    case 1n+xp 0n:
      Empty.absurd({Nat.is_lt(1n+xp, 1n) == True{} : Bool}, un.ft(h))
    case 1n+xp 1n+yp:
      un.lt_succ_r(xp, yp, h)

Uses (5):
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&name=un.ft