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Proof step 12 from proof le-pos-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
i ≤ i0, j < j0, i0 ≠ 0, 0 ≤ i, 0 ≤ j ⊦ ¬ i0 * j0 ≤ i * j
Proof step 14:
0 < i, i0 < i, 0 ≤ i1, i ^ i1 * i ≤ i0 ^ i1 * i0, 0 ≤ i0, 0 ≤ i, ∀ j0, i, i0. i→n(j0) < i→n(i1 + 1) → 0 < i ∧ i0 < i ∧ 0 < j0 ∧ i ^ j0 ≤ i0 ^ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i0 ∧ 0 ≤ i → false ⊦ 0 < i1 ∧ i ^ i1 ≤ i0 ^ i1, i0 ^ i1 ≤ i ^ i1 ∧ i0 < i ∧ i ^ i1 ≠ 0 ∧ 0 ≤ i0 ^ i1 ∧ 0 ≤ i0

Rule argument

spec: int-mult name: pnle-pos seq: i ≤ i0, j < j0, i0 ≠ 0, 0 ≤ i, 0 ≤ j ⊦ ¬ i0 * j0 ≤ i * j subst: [j, i, j0, i0] → [i0, i0 ^ i1, i, i ^ i1] flags: <all paths>

Additional information

Used terms: i0, i0 ^ i1, i, i ^ i1