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Proof step 2 from proof coef-fac-divides (previous step)

j ≤ i, 0 < j, 0 < i ⊦ fac(j) * fac(i - j) | fac(i)

User applied rule induction

And obtained the following new goals

Proof step 3:
j ≤ i ∧ 0 < j ∧ 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ fac(j) * fac(i - j) | fac(i)

Rule argument

indvar: i→n(i) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i)