NatOrder.equal_of_is_eq: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 21-28 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=21&end_line=28

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

def equal_of_is_eq(+left: Nat,+right: Nat,equal: {Nat.is_eq(left,right) == True{} : Bool}) -> {left == right : Nat}:
  match left right:
    case 0n 0n: {==}
    case 0n 1n+rest: Empty.absurd({0n == 1n+rest : Nat},WordEncoding.false_true(equal))
    case 1n+rest 0n: Empty.absurd({1n+rest == 0n : Nat},WordEncoding.false_true(equal))
    case 1n+ +previous 1n+ +last:
      %equal_of_is_eq(previous,last,equal) : {1n+previous == 1n+_ : Nat}
      {==}

Uses (5):
  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_eq
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true