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Proof step 2 from proof prime-fac-divides-01 (previous step)

prime(i) ⊦ i | fac(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → fac(i) = i * fac(i - 1)

Rule argument

spec: inst: name: fac-rec seq: ⊦ 0 < i → fac(i) = i * fac(i - 1) subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0); from specification int-gcd%div-zero: ⊦ i | i; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: i