Fix32.cshr: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend as Fix32
Lines 232-240 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&start_line=232&end_line=240

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

def 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>}:
  match ok:
    case True{}:
      +hb = Equal.trans(Bool, U32.is_lt(s, 32), Nat.is_lt(vs(s), 32n), True{}, lt32(s), hok)
      +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)))
      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)
    case False{}:
      +hb = Equal.trans(Bool, U32.is_lt(s, 32), Nat.is_lt(vs(s), 32n), False{}, lt32(s), hok)
      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))))

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&name=am_small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&name=lt32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend&name=vs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&name=bnot_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&name=none_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend&name=some_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/shrn.bend&name=shrn_high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=keep
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=mval
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=u32_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/fixed.bend&name=opt