def cshr

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:232

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/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/shrn.bend as SHN
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

232def cshr(+a: U32, +s: U32, +ok: Bool, +hok: {Nat.is_lt(vs(s), 32n) == ok : Bool}) -> {SF.mval(~U32, ~SG.u32_val, F.opt(U32, Bool.not(U32.is_lt(s, 32)), U32.shrn(a, U32.to_nat(U32.and(s, 31))))) == SF.keep(ok, C.high(vs(s), SG.u32_val(a))) : Maybe<&2, Nat>}:
233  match ok:
234    case True{}:
235      +hb = Equal.trans(Bool, U32.is_lt(s, 32), Nat.is_lt(vs(s), 32n), True{}, lt32(s), hok)
236      +ev = Equal.trans(Nat, SG.u32_val(U32.shrn(a, U32.to_nat(U32.and(s, 31)))), SG.u32_val(U32.shrn(a, vs(s))), C.high(vs(s), SG.u32_val(a)), Equal.cong(Nat, Nat, t => SG.u32_val(U32.shrn(a, t)), U32.to_nat(U32.and(s, 31)), vs(s), am_small(s, hok)), SHN.shrn_high(a, vs(s)))
237      G.some_of(~U32, ~SG.u32_val, Bool.not(U32.is_lt(s, 32)), G.bnot_eq(U32.is_lt(s, 32), True{}, hb), U32.shrn(a, U32.to_nat(U32.and(s, 31))), C.high(vs(s), SG.u32_val(a)), ev)
238    case False{}:
239      +hb = Equal.trans(Bool, U32.is_lt(s, 32), Nat.is_lt(vs(s), 32n), False{}, lt32(s), hok)
240      G.none_of(~U32, ~SG.u32_val, Bool.not(U32.is_lt(s, 32)), G.bnot_eq(U32.is_lt(s, 32), False{}, hb), U32.shrn(a, U32.to_nat(U32.and(s, 31))))