def andv0

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/f64bits.bend:303

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

303def andv0(+h: U32) -> {v(U32.and(h, U32{WD.pw(32n, 31n)})) == C.shift(31n, C.high(31n, v(h))) : Nat}:
304  match h:
305    case U32{+w}:
306      +m = Word.and(32n, w, WD.pw(32n, 31n))
307      +e0 = Equal.sym(Nat, v(U32{w}), S.unsigned(32n, w), U.to_nat_word(w))
308      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)))