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Proof step 2 from proof zero-ge-add-01 (previous step)

0 ≤ j, 0 ≤ j0, 0 ≤ i0 ⊦ 0 ≤ i0 * j + j0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: zero-ls-02: ⊦ 0 ≤ i → (i * j < 0 ↔ j < 0 ∧ i ≠ 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i ≤ j → (j < i ↔ false); (as)% ⊦ i + j < j ↔ i < 0; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)