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Proof step 2 from proof nummult-ls-02 (previous step)

0 < i, 0 ≤ j ⊦ j < i * i0 ↔ j / i < i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: mult-ls: ⊦ 0 < j ∧ i / j < i0 → i < i0 * j;%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ 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)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult