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Proof step 13 from proof modmod-mult (previous step)

0 < j, j0 < j, j1 < j, 0 ≤ i2, 0 ≤ j0, 0 ≤ j1, 0 ≤ i1 ⊦ (j0 * j1) % j = ((i1 * i2 * j + i1 * j1 + j0 * i2) * j + j0 * j1) % j, 0 ≤ (i1 * i2 * j + i1 * j1 + j0 * i2) * j + j0 * j1 ∧ 0 < j ∧ 0 ≤ j0 * j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ 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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i * j + i * j0 = i * (j + j0); (s)