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Proof step 7 from proof le-pos-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 < j, i0 < i, 0 < i, 0 ≤ i, 0 ≤ i0, 0 ≤ j, i ^ j ≤ i0 ^ j, ∀ j0, i, i0. i→n(j0) < i→n(j) → 0 < i ∧ i0 < i ∧ 0 < j0 ∧ i ^ j0 ≤ i0 ^ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i0 ∧ 0 ≤ i → false ⊦

Proof step 7 from proof le-pos-01 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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