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Proof step 33 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, 0 ≤ i0, i0 * j + j0 ≤ (j0 * i1) / j + i0 * i1, 0 ≤ i0 * j + j0, 0 ≤ (j0 * i1) / j + i0 * i1, 0 < j0 ∧ j0 < j ∧ 0 < i1 ∧ i1 < j → (j0 * i1) / j < j0, j0 = 0 ∨ 0 ≤ i1, i0 = 0 ∨ 0 ≤ i1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
0 < i0 * j + j0, 0 < j1, i1 < j, j0 < j, 0 < j, 0 < (j0 * i1) / j + i0 * i1, i0 * j + j0 ≤ (j0 * i1) / j + i0 * i1, 0 ≤ i0, 0 ≤ j0, 0 ≤ (j0 * i1) / j + i0 * i1, i0 = 0 ∨ 0 ≤ i1, j0 = 0 ∨ 0 ≤ i1 ⊦

Rule argument

Additional information

Used simplifier rules: prod-div-less-01: ⊦ 0 < i ∧ i < j ∧ 0 < i1 ∧ i1 < j → (i * i1) / j < i1;%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); (s)