def xorv0

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64bits.bend:293

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

293def xorv0(+h: U32) -> {v(U32.xor(h, U32{WD.pw(32n, 31n)})) == Nat.add(C.low(31n, v(h)), C.shift(31n, Nat.sub(1n, C.high(31n, v(h))))) : Nat}:
294  match h:
295    case U32{+w}:
296      +m = Word.xor(32n, w, WD.pw(32n, 31n))
297      +e0 = Equal.sym(Nat, v(U32{w}), S.unsigned(32n, w), U.to_nat_word(w))
298      Equal.trans(Nat, U32.to_nat(U32{m}), S.unsigned(32n, m), Nat.add(C.low(31n, v(U32{w})), C.shift(31n, Nat.sub(1n, C.high(31n, v(U32{w}))))), U.to_nat_word(m), Equal.trans(Nat, S.unsigned(32n, m), Nat.add(C.low(31n, S.unsigned(32n, w)), C.shift(31n, Nat.sub(1n, C.high(31n, S.unsigned(32n, w))))), Nat.add(C.low(31n, v(U32{w})), C.shift(31n, Nat.sub(1n, C.high(31n, v(U32{w}))))), xtop(31n, w), Equal.cong(Nat, Nat, z => Nat.add(C.low(31n, z), C.shift(31n, Nat.sub(1n, C.high(31n, z)))), S.unsigned(32n, w), v(U32{w}), e0)))