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Proof step 1 from proof pls-pos-02 (conclusion)

⊦ i < i0 * j ∧ j ≤ j0 ∧ 0 ≤ i0 → i < i0 * j0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ls-forward: ⊦ i * j < i * j0 → i ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs