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Proof step 6 from proof mult-gt-both (previous step)

0 < i1, 0 < j1, i < i1, j < j1, i1 * j ≤ i * j, 0 ≤ i, 0 ≤ j, 0 ≤ i1, 0 ≤ j1, i1 * j1 ≤ i * j ⊦ i * j < i * j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j < j1, i < i1, 0 < j1, 0 < i1, i1 * j1 ≤ i * j, 0 ≤ j1, 0 ≤ i1, 0 ≤ j, 0 ≤ i, i1 * j ≤ i * j, i * j1 ≤ i * j ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)