NatOrder.digit_lt: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 251-265 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=251&end_line=265

import Base
import stelliferous@0.0.2.0/proofs/u32_comparison.bend as Comparison
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def digit_lt(+a: Nat,+b: Nat,+bit: Bool,h: {Nat.is_lt(a,b) == True{} : Bool}) -> {Nat.is_lt(Comparison.digit(bit,a),
    Nat.double(b)) == True{} : Bool}:
  match a b bit:
    case 0n 0n bit:
      Empty.absurd({Nat.is_lt(Comparison.digit(bit,0n),0n) == True{} : Bool},WordEncoding.false_true(h))
    case 0n 1n+b False{}:
      {==}
    case 0n 1n+b True{}:
      {==}
    case 1n+a 0n bit:
      Empty.absurd({Nat.is_lt(Comparison.digit(bit,1n+a),0n) == True{} : Bool},WordEncoding.false_true(h))
    case 1n+a 1n+b False{}:
      digit_lt(a,b,False{},h)
    case 1n+a 1n+b True{}:
      digit_lt(a,b,True{},h)

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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/u32_comparison.bend&name=digit
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true