F64bits.andv0: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as F64bits
Lines 303-308 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend&start_line=303&end_line=308

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

def andv0(+h: U32) -> {v(U32.and(h, U32{WD.pw(32n, 31n)})) == C.shift(31n, C.high(31n, v(h))) : Nat}:
  match h:
    case U32{+w}:
      +m = Word.and(32n, w, WD.pw(32n, 31n))
      +e0 = Equal.sym(Nat, v(U32{w}), S.unsigned(32n, w), U.to_nat_word(w))
      Equal.trans(Nat, U32.to_nat(U32{m}), S.unsigned(32n, m), C.shift(31n, C.high(31n, v(U32{w}))), U.to_nat_word(m), Equal.trans(Nat, S.unsigned(32n, m), C.shift(31n, C.high(31n, S.unsigned(32n, w))), C.shift(31n, C.high(31n, v(U32{w}))), atop(31n, w), Equal.cong(Nat, Nat, z => C.shift(31n, C.high(31n, z)), S.unsigned(32n, w), v(U32{w}), e0)))

Uses (15):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.and
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=to_nat_word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=pw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend&name=atop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift