Nat.le_lt_succ: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 107-114 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=107&end_line=114

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def le_lt_succ(+a: Nat, +b: Nat, e: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_lt(a, 1n+b) == True{} : Bool}:
  match a b:
    case 0n _:
      {==}
    case 1n+p 0n:
      Empty.absurd({Nat.is_lt(1n+p, 1n) == True{} : Bool}, L.false_true(e))
    case 1n+p 1n+q:
      le_lt_succ(p, q, e)

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-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true