def AP.lt_succ_l

bend-osdev-array@0.1.0.1 · PROOF.bend:756

import Base

756def AP.lt_succ_l(x: Nat, y: Nat, h: {Nat.is_lt(1n+x, y) == True{} : Bool}) -> {Nat.is_lt(x, y) == True{} : Bool}:
757  match x y:
758    case 0n 0n:
759      Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, AP.ft(h))
760    case 0n 1n+q:
761      {==}
762    case 1n+p 0n:
763      Empty.absurd({Nat.is_lt(1n+p, 0n) == True{} : Bool}, AP.ft(h))
764    case 1n+p 1n+q:
765      AP.lt_succ_l(p, q, h)