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Proof step 11 from proof ls-pos-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: notneg: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i ^ j < 0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss) Used terms: i, i ^ i1, i0, i0 ^ i1