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Proof step 8 from proof le-pos-01 (previous step)

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 ⊦ 0 < j - 1 ∧ 0 ≤ i0 ∧ 0 ≤ i ∧ i ^ (j - 1) ≤ i0 ^ (j - 1) ∧ i0 < i ∧ 0 ≤ j - 1 ∧ 0 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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 ⊦ 1 < j ∧ i ^ (j - 1) ≤ i0 ^ (j - 1)

Rule argument

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs