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Proof step 10 from proof mult-02 (previous step)

(i1 * j0 + j1) * j + i0 = i2 * j0 * j + j2, j2 < j0 * j, 0 ≤ j1, 0 ≤ i1, j1 < j0, 0 ≤ i0, i0 < j, 0 < j0, 0 ≤ j2, 0 < j ⊦ i1 * j0 * j + j1 * j + i0 = i2 * j0 * j + j2 ∧ 0 ≤ j1 * j + i0 ∧ j1 * j + i0 < j0 * j, i2 = i1

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%dist-rmerge: ⊦ i * j + i * j0 = i * (j + j0); from specification int-mult