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Proof step 35 from proof less-mult-div-01 (previous step)

0 < (j0 * i1) / j + i0 * i1, 0 < j, j0 < j, i1 < j, 0 < j1, 0 < i0 * j + j0, 0 ≤ (j0 * i1) / j + i0 * i1, 0 ≤ j0, 0 ≤ i0, i0 * j + j0 ≤ (j0 * i1) / j + i0 * i1, j0 = 0 ∨ 0 ≤ i1, i0 = 0 ∨ 0 ≤ i1 ⊦ j0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
1 < j, 0 < j0, 0 < (j0 * i1) / j + i0 * i1, 0 < j, j0 < j, i1 < j, 0 < j1, 0 < i0 * j + j0, 0 ≤ i1, 0 ≤ i0, i0 * j + j0 ≤ (j0 * i1) / j + i0 * i1, 0 ≤ (j0 * i1) / j + i0 * i1 ⊦ j0 = 0

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%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 ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)