def c61

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64adda.bend:35

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 WU
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
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/f64bits.bend as FB

35def c61(+one: Nat, +h1: {one == 1n : Nat}, +c: U32, +hc: {c == U32{WD.pw(32n, 29n)} : U32}) -> {SW.value(WU.U64{0, c}) == C.shift(61n, one) : Nat}:
36  Equal.trans(Nat, C.shift(32n, v(c)), C.shift(32n, C.shift(29n, one)), C.shift(61n, one), Equal.cong(Nat, Nat, z => C.shift(32n, z), v(c), C.shift(29n, one), FB.pwv(29n, {==}, one, h1, c, hc)), Equal.sym(Nat, C.shift(61n, one), C.shift(32n, C.shift(29n, one)), WW.shift_comp(32n, 29n, one)))