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Proof step 2 from proof prod-div-less (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 < (i * i1) / j, 1 < j, 0 < i, i < j, 0 < i1, i1 < j, 0 < j, i ≤ (i * i1) / j ⊦

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)