Wrappers.lt_pos: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend as Wrappers
Lines 256-263 of bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend&start_line=256&end_line=263

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

def lt_pos(+a: Nat, +b: Nat, +h: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_lt(0n, Nat.sub(b, a)) == True{} : Bool}:
  match a b:
    case _ 0n:
      Empty.absurd({Nat.is_lt(0n, Nat.sub(0n, a)) == True{} : Bool}, N.lt_zero_absurd(a, h))
    case 0n 1n+q:
      {==}
    case 1n+p 1n+q:
      lt_pos(p, q, h)

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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd