def topw

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:47

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/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/w64est.bend as WE
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/fixgen.bend as G

47def topw(+one: Nat, +h1: {one == 1n : Nat}, +w: U32, +pw: {w == U32{WD.mask(32n, 32n)} : U32}) -> {Bool.and(C.fits(32n, SG.u32_val(w)), Bool.not(C.fits(32n, 1n+SG.u32_val(w)))) == True{} : Bool}:
48  +S = C.shift(32n, one)
49  +e1 = Equal.cong(Nat, Bool, t => C.fits(32n, t), 1n+SG.u32_val(w), S, WE.m32(one, h1, w, pw))
50  +e2 = Equal.cong(Nat, Bool, t => C.fits(32n, t), S, Nat.add(0n, S), Equal.sym(Nat, Nat.add(0n, S), S, zero_add(S)))
51  G.top_ok(32n, SG.u32_val(w), LW.vb(w), Equal.trans(Bool, C.fits(32n, 1n+SG.u32_val(w)), C.fits(32n, S), False{}, e1, Equal.trans(Bool, C.fits(32n, S), C.fits(32n, Nat.add(0n, S)), False{}, e2, WW.unfit_one(32n, one, h1, 0n))))