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Proof step 5 from proof le-pos-01 (previous step)

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

User applied rule induction

And obtained the following new goals

Proof step 6:
0 < j ∧ 0 ≤ i0 ∧ 0 ≤ i ∧ i ^ j ≤ i0 ^ j ∧ i0 < i ∧ 0 ≤ j ∧ 0 < i, ∀ j0, i0, i. i→n(j0) < i→n(j) → 0 < j0 ∧ 0 ≤ i0 ∧ 0 ≤ i ∧ i ^ j0 ≤ i0 ^ j0 ∧ i0 < i ∧ 0 ≤ j0 ∧ 0 < i → false ⊦ false

Rule argument

indvar: i→n(j) wfpred: <

Additional information

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