def comb_checked

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:1337

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/src/math/generic.bend as G
import bend-collections-laws-math@1.0.0.0/src/math/num.bend as NM
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/src/math/instances.bend as I
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend as FA
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S

1337def comb_checked(+n: WU.U64, +k: WU.U64) -> SG.Comb.checked(~WU.U64, ~I.u64_op, ~I.u64_is, ~SG.u64_val, ~SG.u64_of, 64n, n, k):
1338  Equal.trans(Result<&2, &2, NM.NumError, WU.U64>, G.comb_big(~WU.U64, ~I.u64_op, ~I.u64_is, n, k, I.u64_is(NM.Lt{n, k})), SG.checked(~WU.U64, ~SG.u64_of, 64n, S.choose(v(n), v(k))), SG.checked(~WU.U64, ~SG.u64_of, 64n, M.comb(v(n), v(k))), comb_top(64n, {==}, n, k, I.u64_is(NM.Lt{n, k}), {==}), Equal.cong(Nat, Result<&2, &2, NM.NumError, WU.U64>, t => SG.checked(~WU.U64, ~SG.u64_of, 64n, t), S.choose(v(n), v(k)), M.comb(v(n), v(k)), Equal.sym(Nat, M.comb(v(n), v(k)), S.choose(v(n), v(k)), FA.comb_ok(v(n), v(k)))))