PROOFText.wsh.m0: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 393-399 of bend-osdev-word64@0.1.1.0/PROOF_text.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&start_line=393&end_line=399

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# 10 x + y = 0: x = 0
def wsh.m0(x: Nat, +y: Nat, e: {Nat.add(Nat.mul(x, 10n), y) == 0n : Nat}) -> {x == 0n : Nat}:
  match x:
    case 0n:
      {==}
    case 1n+ +p:
      Empty.absurd({1n+p == 0n : Nat}, UL.nat_succ_add_absurd(Nat.add(Nat.add(9n, Nat.mul(p, 10n)), y), 0n, Equal.trans(Nat, Nat.add(Nat.add(Nat.add(9n, Nat.mul(p, 10n)), y), 1n), Nat.add(Nat.mul(1n+p, 10n), y), 0n, wr.t10(p, y), e)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_succ_add_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&name=wr.t10