def topw

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:58

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/generic.bend as SG
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/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64laws.bend as LV
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

58def topw(+one: Nat, +h1: {one == 1n : Nat}, +w: U32, +pw: {w == U32{WD.mask(32n, 32n)} : U32}) -> {Bool.and(C.fits(64n, SG.u64_val(WU.U64{w, w})), Bool.not(C.fits(64n, 1n+SG.u64_val(WU.U64{w, w})))) == True{} : Bool}:
59  +m = {WU.U64{w, w} : WU.U64}
60  +S = C.shift(64n, one)
61  +e1 = Equal.cong(Nat, Bool, t => C.fits(64n, t), 1n+SG.u64_val(m), S, top1w(one, h1, w, pw))
62  +e2 = Equal.cong(Nat, Bool, t => C.fits(64n, t), S, Nat.add(0n, S), Equal.sym(Nat, Nat.add(0n, S), S, zero_add(S)))
63  G.top_ok(64n, SG.u64_val(m), LV.vb(m), Equal.trans(Bool, C.fits(64n, 1n+SG.u64_val(m)), C.fits(64n, S), False{}, e1, Equal.trans(Bool, C.fits(64n, S), C.fits(64n, Nat.add(0n, S)), False{}, e2, WW.unfit_one(64n, one, h1, 0n))))