Fact.factorial_go: 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 25-30 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=25&end_line=30

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A
import bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-crypto@1.0.0.0/spec/math/natural.bend as S

def factorial_go(+n: Nat, +acc: Nat) -> {M.factorial_go(n, acc) == Nat.mul(acc, S.factorial(n)) : Nat}:
  match n:
    case 0n:
      Equal.sym(Nat, Nat.mul(acc, 1n), acc, A.mul_one(acc))
    case 1n+ +p:
      Equal.trans(Nat, M.factorial_go(p, Nat.mul(1n+p, acc)), Nat.mul(Nat.mul(1n+p, acc), S.factorial(p)), Nat.mul(acc, Nat.mul(1n+p, S.factorial(p))), factorial_go(p, Nat.mul(1n+p, acc)), mul_left_comm(1n+p, acc, S.factorial(p)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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/lib/lemmas/proofs/nat_algebra.bend&name=mul_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend&name=mul_left_comm
  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_go