def andm0

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/f64bits.bend:48

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

48def andm0(+x: U32, +k: Nat) -> {v(U32.and(x, U32{WD.mask(32n, k)})) == C.low(k, v(x)) : Nat}:
49  match x:
50    case U32{+w}:
51      +m = Word.and(32n, w, WD.mask(32n, k))
52      Equal.trans(Nat, U32.to_nat(U32{m}), S.unsigned(32n, m), C.low(k, v(U32{w})), U.to_nat_word(m), Equal.trans(Nat, S.unsigned(32n, m), C.low(k, S.unsigned(32n, w)), C.low(k, v(U32{w})), andw(32n, k, w), Equal.cong(Nat, Nat, z => C.low(k, z), S.unsigned(32n, w), v(U32{w}), Equal.sym(Nat, v(U32{w}), S.unsigned(32n, w), U.to_nat_word(w)))))