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Proof step 2 from proof mult-add-greater (previous step)

(i + j) * i1 < i * i1, 0 < i, 0 < j, 0 < i1 ⊦

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i < j → ¬ j < i; (s)% ⊦ i + j < j ↔ i < 0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2