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Proof step 9 from proof ls-pos-02 (previous step)

0 ≤ i1, i0 ^ (i1 + 1) < i ^ (i1 + 1), i ≤ i0, 0 ≤ i0, 0 ≤ i, ~1 ≤ i1, ∀ j0, i0, i. i→n(j0) < i→n(i1 + 1) → i0 ^ j0 < i ^ j0 ∧ i ≤ i0 ∧ 0 ≤ i0 ∧ 0 ≤ i ∧ 0 ≤ j0 → false ⊦ i0 ^ i1 < i ^ i1 ∧ 0 ≤ i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: succ: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ 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