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Proof step 6 from proof modmod-mult-04 (previous step)

j1 = i1 * j + j2 ∧ 0 ≤ j2 ∧ j2 < j, 0 ≤ i0, j1 < j * j0, 0 ≤ j1, 0 < j, 0 < j0 ⊦ j2 = (i0 * j * j0 + j1) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j0, 0 ≤ j2, j2 < j, 0 ≤ i0, i1 * j + j2 < j * j0, 0 ≤ i1, 0 < j ⊦ j2 = (j * (i1 + i0 * j0) + j2) % j

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%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%dist-rmerge: ⊦ i * j + i * j0 = i * (j + j0); from specification int-mult