NatOrder.sub_lt: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 213-223 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=213&end_line=223

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

def sub_lt(+a: Nat,+b: Nat,+c: Nat,order: {Nat.is_le(b,a) == True{} : Bool},bound: {Nat.is_lt(a,Nat.add(b,
        c)) == True{} : Bool}) -> {Nat.is_lt(Nat.sub(a,b),c) == True{} : Bool}:
  match a b:
    case 0n 0n:
      bound
    case 0n 1n+b:
      Empty.absurd({Nat.is_lt(0n,c) == True{} : Bool},WordEncoding.false_true(order))
    case 1n+a 0n:
      bound
    case 1n+a 1n+b:
      sub_lt(a,b,c,order,bound)

Uses (8):
  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.add
  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=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