def milliseconds

bend-collections-laws-crypto@1.0.0.0 · proofs/math/u64/u64div.bend:371

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as U
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/math/u64/u64.bend as P
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/types/model.bend as T

371# THEOREM: dividing by 10^6 is the specification's nanoseconds-to-milliseconds.
372def milliseconds(+a: U.U64) -> {T.I64{P.bits(U.div_small_signed(a, 1000000))} == S.milliseconds(T.I64{P.bits(a)}) : T.Int64}:
373  Equal.cong(Word(64n), T.Int64, z => T.I64{z}, P.bits(U.div_small_signed(a, 1000000)), S.quotient_signed(P.bits(a), S.negative(P.bits(a))), Equal.trans(Word(64n), P.bits(U.div_small_signed(a, 1000000)), qs(P.bits(a), S.negative(P.bits(a)), 1000000), S.quotient_signed(P.bits(a), S.negative(P.bits(a))), div_signed(a, 1000000, {==}, {==}), qs_spec(P.bits(a), S.negative(P.bits(a)))))