PROOFText.wsh.vz: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 390-391 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=390&end_line=391

import Base
import bend-osdev-word64@0.1.1.0/word64.bend as W
import bend-osdev-word64@0.1.1.0/LAWS.bend as WB

def wsh.vz(+a: W.W64, e: {W.W64.to_nat(a) == 0n : Nat}) -> {W.W64.is_zero(a) == True{} : Bool}:
  Equal.trans(Bool, W.W64.is_zero(a), Nat.is_eq(W.W64.to_nat(a), 0n), True{}, WB.eq_value(a, W.W64.zero()), Equal.cong(Nat, Bool, zz => Nat.is_eq(zz, 0n), W.W64.to_nat(a), 0n, e))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/LAWS.bend&name=eq_value
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/word64.bend&name=W64.zero