def low63_v

bend-collections-laws-math@1.0.0.0 · proofs/math/random/wrappers.bend:53

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/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

53def low63_v(+l: U32, +h: U32) -> {SW.value(W.U64{l, U32.and(h, 2147483647)}) == C.low(63n, val(l, h)) : Nat}:
54  +n = val(l, h)
55  Equal.trans(Nat, Nat.add(v(l), C.shift(32n, v(U32.and(h, 2147483647)))), Nat.add(v(l), C.shift(32n, C.low(31n, v(h)))), C.low(63n, n),
56    Equal.cong(Nat, Nat, z => Nat.add(v(l), C.shift(32n, z)), v(U32.and(h, 2147483647)), C.low(31n, v(h)), FB.andm(h, 31n, 2147483647, {==})),
57    Equal.sym(Nat, C.low(63n, n), Nat.add(v(l), C.shift(32n, C.low(31n, v(h)))),
58      Equal.trans(Nat, C.low(63n, n), Nat.add(C.low(32n, n), C.shift(32n, C.low(31n, C.high(32n, n)))), Nat.add(v(l), C.shift(32n, C.low(31n, v(h)))),
59        FB.low_split(32n, 31n, n),
60        Equal.trans(Nat, Nat.add(C.low(32n, n), C.shift(32n, C.low(31n, C.high(32n, n)))), Nat.add(v(l), C.shift(32n, C.low(31n, C.high(32n, n)))), Nat.add(v(l), C.shift(32n, C.low(31n, v(h)))),
61          Equal.cong(Nat, Nat, z => Nat.add(z, C.shift(32n, C.low(31n, C.high(32n, n)))), C.low(32n, n), v(l), WW.low_u(32n, v(l), v(h), LW.vb(l))),
62          Equal.cong(Nat, Nat, z => Nat.add(v(l), C.shift(32n, C.low(31n, z))), C.high(32n, n), v(h), WW.high_u(32n, v(l), v(h), LW.vb(l)))))))