def spow

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:243

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

243def 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}:
244  match ok:
245    case True{}:
246      %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}
247      %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}
248      %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}
249      N.is_eq_refl(pw(a, e))
250    case False{}:
251      %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}
252      %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}
253      ht