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Proof step 3 from proof ls-pos-02 (previous step)

i0 ^ j < i ^ j, i ≤ i0, 0 ≤ j, 0 ≤ i, 0 ≤ i0 ⊦

User applied rule induction

And obtained the following new goals

Proof step 4:
i0 ^ j < i ^ j, i ≤ i0, 0 ≤ j, 0 ≤ i, 0 ≤ i0, ∀ j0, i0, i. i→n(j0) < i→n(j) → i0 ^ j0 < i ^ j0 ∧ i ≤ i0 ∧ 0 ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ i0 → false ⊦

Rule argument

indvar: i→n(j) wfpred: <

Additional information

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