Fact.factorial_ok: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend as Fact
Lines 32-34 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend&start_line=32&end_line=34

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

# factorial(n) == n!
def factorial_ok(+n: Nat) -> {M.factorial(n) == S.factorial(n) : Nat}:
  Equal.trans(Nat, M.factorial(n), Nat.mul(1n, S.factorial(n)), S.factorial(n), factorial_go(n, 1n), LC.one_mul(S.factorial(n)))

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-crypto@1.0.0.0/proofs/math/natural/fact.bend&name=factorial_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend&name=one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/natural.bend&name=factorial
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=factorial