PROOF.h.wcmp_sound: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1798-1812 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=1798&end_line=1812

import Base

def h.wcmp_sound(+n: Nat, a: Word(n), b: Word(n), +e: {Cmp.is_eq(Word.cmp(n, a, b)) == True{} : Bool})
  -> {a == b : Word(n)}:
  match n:
    case 0n:
      match a b:
        case WNil{} WNil{}:
          {==}
    case 1n+p:
      match a b:
        case WCon{+x, +at} WCon{+y, +bt}:
          +e1 = h.fin_hd(Word.cmp(p, at, bt), x, y, e)
          +e2 = h.wcmp_sound(p, at, bt, h.fin_eq(Word.cmp(p, at, bt), x, y, e))
          %e1 : {WCon{x, at} == WCon{_, bt} : Word(1n+p)}
          %e2 : {WCon{x, at} == WCon{x, _} : Word(1n+p)}
          {==}

Uses (9):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.fin_eq
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.fin_hd