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Proof step 1 from proof div-mult-nle-est (conclusion)

0 < i, 0 ≤ j ⊦ ¬ j / i ≤ i0 → ¬ j ≤ i * i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < i, i0 < j / i, j ≤ i * i0, 0 ≤ j, 0 ≤ i0, 0 < j / i ⊦

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ 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%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs