PROOF.nat.le_succ: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 98-105 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=98&end_line=105

import Base

def nat.le_succ(a: Nat, b: Nat, e: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_le(a, 1n+b) == True{} : Bool}:
  match a b:
    case 0n _:
      {==}
    case 1n+ap 0n:
      Empty.absurd({Nat.is_le(1n+ap, 1n) == True{} : Bool}, absurd.ft(e))
    case 1n+ap 1n+bp:
      nat.le_succ(ap, bp, e)

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_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=absurd.ft