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Proof step 4 from proof less-mult-div-01 (previous step)

i1 < j, i ≤ (i * i1) / j, 0 < i, 0 < j, 0 < j1, 0 < (i * i1) / j ⊦ 0 < j ∧ 0 < i * i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i ≤ (i * i1) / j, 0 < i, 0 < j, 0 < j1, 0 < (i * i1) / j, i1 ≤ 0, i1 < i, i1 < j, i1 < j1, i1 < (i * i1) / j ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult