NatOrder.positive_difference: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 57-62 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=57&end_line=62

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def positive_difference(+end: Nat,+begin: Nat,positive: {Nat.is_lt(begin,end) == True{} : Bool}) -> {Nat.is_lt(0n,Nat.sub(end,begin)) == True{} : Bool}:
  match end begin:
    case 0n 0n: Empty.absurd({False{} == True{} : Bool},WordEncoding.false_true(positive))
    case 0n 1n+begin: Empty.absurd({False{} == True{} : Bool},WordEncoding.false_true(positive))
    case 1n+end 0n: {==}
    case 1n+end 1n+begin: positive_difference(end,begin,positive)

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=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true