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Proof step 1 from proof estimate-01 (conclusion)

0 < i, 0 < i0, 0 < j, j < i, j0 < i0 ⊦ j0 < (i * i0) / j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
j < i, j0 < i0, (i * i0) / j ≤ j0, 0 < i0, 0 < j, 0 < i, 1 < i, (i * i0) / j < i0 ⊦

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-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs