def cshr

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:208

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/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

208def cshr(+a: WU.U64, +s: U32, +ok: Bool, +hok: {Nat.is_lt(vs(s), 64n) == ok : Bool}) -> {SF.mval(~WU.U64, ~SG.u64_val, F.opt(WU.U64, Bool.not(U32.is_lt(s, 64)), X.shr(a, U32.to_nat(U32.and(s, 63))))) == SF.keep(ok, C.high(vs(s), SG.u64_val(a))) : Maybe<&2, Nat>}:
209  match ok:
210    case True{}:
211      +hb = Equal.trans(Bool, U32.is_lt(s, 64), Nat.is_lt(vs(s), 64n), ok, lt64(s), hok)
212      +ev = Equal.trans(Nat, SG.u64_val(X.shr(a, U32.to_nat(U32.and(s, 63)))), SG.u64_val(X.shr(a, vs(s))), C.high(vs(s), SG.u64_val(a)), Equal.cong(Nat, Nat, t => SG.u64_val(X.shr(a, t)), U32.to_nat(U32.and(s, 63)), vs(s), am_small(s, hok)), SH.shr_value(a, vs(s)))
213      G.some_of(~WU.U64, ~SG.u64_val, Bool.not(U32.is_lt(s, 64)), G.bnot_eq(U32.is_lt(s, 64), True{}, hb), X.shr(a, U32.to_nat(U32.and(s, 63))), C.high(vs(s), SG.u64_val(a)), ev)
214    case False{}:
215      +hb = Equal.trans(Bool, U32.is_lt(s, 64), Nat.is_lt(vs(s), 64n), ok, lt64(s), hok)
216      G.none_of(~WU.U64, ~SG.u64_val, Bool.not(U32.is_lt(s, 64)), G.bnot_eq(U32.is_lt(s, 64), False{}, hb), X.shr(a, U32.to_nat(U32.and(s, 63))))