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Proof step 12 from proof est-4-big-02 (previous step)

0 ≤ i0, 1 < j, 0 < j, 0 < i0, 0 < j0, 0 ≤ j0, j ≤ 2 * j0, 2 < i0 * j + j0, j ≤ i0 * j + j0, (i0 * j) * 2 + j0 * 2 < 3 * j, j0 < j, 0 < i0 * j + j0, i0 * j < 2 * j0 ⊦ j = 3, j = 2

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: (i0 * j) * 2 + i0 * j < (i0 * j) * 2 + j0 * 2

Additional information

Used simplifier rules: numsucc: ⊦ (* i0) * i + i = (i0 + 1) * 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%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%numls-01: ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: (i0 * j) * 2 + i0 * j < (i0 * j) * 2 + j0 * 2