def perm_ok

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/fact.bend:80

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend as LC
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S

80# perm(n, k) == n.descFactorial(k)
81def perm_ok(+n: Nat, +k: Nat) -> {M.perm(n, k) == S.desc(n, k) : Nat}:
82  Equal.trans(Nat, M.perm(n, k), Nat.mul(1n, S.desc(n, k)), S.desc(n, k), perm_go(k, n, 1n), LC.one_mul(S.desc(n, k)))