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Proof step 13 from proof div-mult-shift-holds (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 ≤ i → (0 ≤ i * j ↔ i = 0 ∨ 0 ≤ j); (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i = i + j ↔ j = 0; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i * 0 = 0; (s)