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Proof step 8 from proof div-mult-02 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i2, i0 * j, i0 * j1, i1, j0]

Additional information

Used simplifier rules: ⊦ i * j + i * j0 = i * (j + j0); (s)%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% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); (s) Used terms: i2, i0 * j, i0 * j1, i1, j0