Fix64.cpow: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend as Fix64
Lines 229-238 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend&start_line=229&end_line=238

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/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/src/math/num.bend as NM
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/u64int.bend as UI

def cpow(+a: WU.U64, +e: U32, +ok: Bool, +hok: {C.fits(64n, pw(a, e)) == ok : Bool}) -> {SF.mval(~WU.U64, ~SG.u64_val, F.res_opt(WU.U64, gpow(a, e))) == SF.keep(ok, pw(a, e)) : Maybe<&2, Nat>}:
  match ok:
    case True{}:
      %Equal.sym(Result<&2, &2, NM.NumError, WU.U64>, gpow(a, e), SG.checked(~WU.U64, ~SG.u64_of, 64n, pw(a, e)), UI.pow_checked(a, vs(e))) : {SF.mval(~WU.U64, ~SG.u64_val, F.res_opt(WU.U64, _)) == Some{pw(a, e)} : Maybe<&2, Nat>}
      %Equal.sym(Bool, C.fits(64n, pw(a, e)), True{}, hok) : {SF.mval(~WU.U64, ~SG.u64_val, F.res_opt(WU.U64, SG.checked_pick(~WU.U64, ~SG.u64_of, pw(a, e), _))) == Some{pw(a, e)} : Maybe<&2, Nat>}
      Equal.cong(Nat, Maybe<&2, Nat>, t => Some{t}, SG.u64_val(SG.u64_of(pw(a, e))), pw(a, e), LV.vo(pw(a, e), hok))
    case False{}:
      %Equal.sym(Result<&2, &2, NM.NumError, WU.U64>, gpow(a, e), SG.checked(~WU.U64, ~SG.u64_of, 64n, pw(a, e)), UI.pow_checked(a, vs(e))) : {SF.mval(~WU.U64, ~SG.u64_val, F.res_opt(WU.U64, _)) == None{} : Maybe<&2, Nat>}
      %Equal.sym(Bool, C.fits(64n, pw(a, e)), False{}, hok) : {SF.mval(~WU.U64, ~SG.u64_val, F.res_opt(WU.U64, SG.checked_pick(~WU.U64, ~SG.u64_of, pw(a, e), _))) == None{} : Maybe<&2, Nat>}
      {==}

Uses (22):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.sym
  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=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend&name=gpow
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend&name=pw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend&name=vs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&name=pow_checked
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64laws.bend&name=vo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  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=checked
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=checked_pick
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=u64_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/generic.bend&name=u64_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/fixed.bend&name=res_opt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/num.bend&name=NumError
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64