def spow

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:267

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/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/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32int.bend as UI

267def spow(+top: U32, +ht: {Bool.and(C.fits(32n, SG.u32_val(top)), Bool.not(C.fits(32n, 1n+SG.u32_val(top)))) == True{} : Bool}, +a: U32, +e: U32, +ok: Bool, +hok: {C.fits(32n, pw(a, e)) == ok : Bool}) -> {SF.saturated(32n, pw(a, e), SG.u32_val(F.or_top(U32, top, F.res_opt(U32, gpow(a, e)))), ok) == True{} : Bool}:
268  match ok:
269    case True{}:
270      %Equal.sym(Result<&2, &2, NM.NumError, U32>, gpow(a, e), SG.checked(~U32, ~SG.u32_of, 32n, pw(a, e)), UI.pow_checked(a, vs(e))) : {SF.saturated(32n, pw(a, e), SG.u32_val(F.or_top(U32, top, F.res_opt(U32, _))), True{}) == True{} : Bool}
271      %Equal.sym(Bool, C.fits(32n, pw(a, e)), True{}, hok) : {SF.saturated(32n, pw(a, e), SG.u32_val(F.or_top(U32, top, F.res_opt(U32, SG.checked_pick(~U32, ~SG.u32_of, pw(a, e), _)))), True{}) == True{} : Bool}
272      %Equal.sym(Nat, SG.u32_val(SG.u32_of(pw(a, e))), pw(a, e), LW.vo(pw(a, e), hok)) : {Nat.is_eq(_, pw(a, e)) == True{} : Bool}
273      N.is_eq_refl(pw(a, e))
274    case False{}:
275      %Equal.sym(Result<&2, &2, NM.NumError, U32>, gpow(a, e), SG.checked(~U32, ~SG.u32_of, 32n, pw(a, e)), UI.pow_checked(a, vs(e))) : {SF.saturated(32n, pw(a, e), SG.u32_val(F.or_top(U32, top, F.res_opt(U32, _))), False{}) == True{} : Bool}
276      %Equal.sym(Bool, C.fits(32n, pw(a, e)), False{}, hok) : {SF.saturated(32n, pw(a, e), SG.u32_val(F.or_top(U32, top, F.res_opt(U32, SG.checked_pick(~U32, ~SG.u32_of, pw(a, e), _)))), False{}) == True{} : Bool}
277      ht