Nat.lt_succ_le: 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 116-123 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=116&end_line=123

import Base

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

Uses (7):
  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/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=zero_le