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Proof step 2 from proof div-est-nle-pos (previous step)

0 < j, i0 ≤ i / j, 0 ≤ i ⊦ i0 * j ≤ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
i < i0 * j, 0 < j, 0 < i / j, 0 < i0, i0 ≤ i / j, 0 ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)