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Proof step 2 from proof fac-le (previous step)

0 < i, 0 < j ⊦ fac(i) ≤ fac(j) ↔ i ≤ j

User applied rule induction

And obtained the following new goals

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

Rule argument

indvar: i→n(i) wfpred: <

Additional information

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