U32div.pos_nat: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend as U32div
Lines 170-175 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&start_line=170&end_line=175

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

def pos_nat(+x: Nat, +h: {Cmp.is_eq(Nat.cmp(x, 0n)) == False{} : Bool}) -> {Nat.is_lt(0n, x) == True{} : Bool}:
  match x:
    case 0n:
      Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, L.true_false(h))
    case 1n+k:
      {==}

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=Cmp.is_eq
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=true_false