Fact.perm_ok: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend as Fact
Lines 80-82 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend&start_line=80&end_line=82

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

# perm(n, k) == n.descFactorial(k)
def perm_ok(+n: Nat, +k: Nat) -> {M.perm(n, k) == S.desc(n, k) : Nat}:
  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)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/fact.bend&name=perm_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend&name=one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=desc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=perm