PROOF.w64.zero: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 560-569 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=560&end_line=569

import Base
import bend-osdev-word64@0.1.0.0/word64.bend as W
import bend-osdev-word64@0.1.0.0/LAWS.bend as WL
import bend-osdev-algo@0.1.0.0/algo.bend as A

def w64.zero(+a: W.W64, +e: {A.bits64.word(a) == Word.zero(64n) : Word(64n)}) -> {a == W.W64.zero() : W.W64}:
  +l = A.bits32.word(W.W64.lo(a))
  +h = A.bits32.word(W.W64.hi(a))
  +c = W.W64.bits.cat(32n, 32n, l, h)
  +el = Equal.trans(Word(32n), l, W.W64.bits.lo(32n, 32n, c), Word.zero(32n), Equal.sym(Word(32n), W.W64.bits.lo(32n, 32n, c), l, w64.lo_cat(32n, 32n, l, h)), Equal.cong(Word(64n), Word(32n), v => W.W64.bits.lo(32n, 32n, v), c, Word.zero(64n), e))
  +eh = Equal.trans(Word(32n), h, W.W64.bits.hi(32n, 32n, c), Word.zero(32n), Equal.sym(Word(32n), W.W64.bits.hi(32n, 32n, c), h, w64.hi_cat(32n, 32n, l, h)), Equal.cong(Word(64n), Word(32n), v => W.W64.bits.hi(32n, 32n, v), c, Word.zero(64n), e))
  %WL.parts_of(a) : {_ == W.W64.zero() : W.W64}
  %Equal.sym(U32, W.W64.hi(a), 0, u32.zero(W.W64.hi(a), eh)) : {W.W64.from_parts(_, W.W64.lo(a)) == W.W64.zero() : W.W64}
  %Equal.sym(U32, W.W64.lo(a), 0, u32.zero(W.W64.lo(a), el)) : {W.W64.from_parts(0, _) == W.W64.zero() : W.W64}
  {==}

Uses (20):
  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.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=w64.hi_cat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=w64.lo_cat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bits32.word
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bits64.word
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/LAWS.bend&name=parts_of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.bits.cat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.bits.hi
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.bits.lo
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.from_parts
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.hi
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.lo
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64.zero