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Proof step 5 from proof less-mult-div-01 (previous step)

0 < (i * i1) / j, 0 < i, 0 < j, 0 < j1, i1 < j, i ≤ (i * i1) / j, 0 ≤ i ∧ 0 < j → (∃ i0, j0. i = i0 * j + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < j) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
j0 < j, i1 < j, 0 < j1, 0 < j, 0 < i0 * j + j0, 0 < ((i0 * j + j0) * i1) / j, 0 ≤ j0, 0 ≤ i0, i0 * j + j0 ≤ ((i0 * j + j0) * i1) / j, 0 ≤ i0 * j + j0, 0 ≤ ((i0 * j + j0) * i1) / j ⊦

Rule argument

Additional information

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