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Proof step 1 from proof prod-div-less (conclusion)

⊦ 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 2:
i < j, i1 < j, i ≤ (i * i1) / j, 0 < i, 0 < i1, 0 < j, 1 < j, 0 < (i * i1) / j ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs