Fix64.spow: 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 243-253 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=243&end_line=253

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/lib/nat.bend as N
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 spow(+top: WU.U64, +ht: {Bool.and(C.fits(64n, SG.u64_val(top)), Bool.not(C.fits(64n, 1n+SG.u64_val(top)))) == True{} : Bool}, +a: WU.U64, +e: U32, +ok: Bool, +hok: {C.fits(64n, pw(a, e)) == ok : Bool}) -> {SF.saturated(64n, pw(a, e), SG.u64_val(F.or_top(WU.U64, top, F.res_opt(WU.U64, gpow(a, e)))), ok) == True{} : Bool}:
  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.saturated(64n, pw(a, e), SG.u64_val(F.or_top(WU.U64, top, F.res_opt(WU.U64, _))), True{}) == True{} : Bool}
      %Equal.sym(Bool, C.fits(64n, pw(a, e)), True{}, hok) : {SF.saturated(64n, pw(a, e), SG.u64_val(F.or_top(WU.U64, top, F.res_opt(WU.U64, SG.checked_pick(~WU.U64, ~SG.u64_of, pw(a, e), _)))), True{}) == True{} : Bool}
      %Equal.sym(Nat, SG.u64_val(SG.u64_of(pw(a, e))), pw(a, e), LV.vo(pw(a, e), hok)) : {Nat.is_eq(_, pw(a, e)) == True{} : Bool}
      N.is_eq_refl(pw(a, e))
    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.saturated(64n, pw(a, e), SG.u64_val(F.or_top(WU.U64, top, F.res_opt(WU.U64, _))), False{}) == True{} : Bool}
      %Equal.sym(Bool, C.fits(64n, pw(a, e)), False{}, hok) : {SF.saturated(64n, pw(a, e), SG.u64_val(F.or_top(WU.U64, top, F.res_opt(WU.U64, SG.checked_pick(~WU.U64, ~SG.u64_of, pw(a, e), _)))), False{}) == True{} : Bool}
      ht

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.and
  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.sym
  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_eq
  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/lib/nat.bend&name=is_eq_refl
  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=saturated
  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=or_top
  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