PROOF.AP.lt_succ_l: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 756-765 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=756&end_line=765

import Base

def AP.lt_succ_l(x: Nat, y: Nat, h: {Nat.is_lt(1n+x, y) == True{} : Bool}) -> {Nat.is_lt(x, y) == True{} : Bool}:
  match x y:
    case 0n 0n:
      Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, AP.ft(h))
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      Empty.absurd({Nat.is_lt(1n+p, 0n) == True{} : Bool}, AP.ft(h))
    case 1n+p 1n+q:
      AP.lt_succ_l(p, q, 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-array@0.1.0.1/PROOF.bend&name=AP.ft