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Proof step 24 from proof pot2-est-div6 (previous step)

j0 < 6, 0 < (3 + i1) * 6 + j0, 0 ≤ j0, 36 ≤ (3 + i1) * 6 + j0, 8 * 2 ^ i1 ≤ (3 + i1) * 6 + j0 + 1, 4 * 2 ^ i1 ≤ 3 * (4 + i1), 0 ≤ i1, 1 + 6 * (3 + i1) + j0 ≤ 6 * i1 + 24 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 25:
6 * i1 + 24 = 6 * (i1 + 4), 0 < (3 + i1) * 6 + j0, j0 < 6, 1 + 6 * (3 + i1) + j0 ≤ 6 * i1 + 24, 0 ≤ i1, 4 * 2 ^ i1 ≤ 3 * (4 + i1), 8 * 2 ^ i1 ≤ (3 + i1) * 6 + j0 + 1, 36 ≤ (3 + i1) * 6 + j0, 0 ≤ j0 ⊦

Rule argument

fma: 6 * i1 + 24 = 6 * (i1 + 4)

Additional information

Used simplifier rules: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = 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 Used formulas: 6 * i1 + 24 = 6 * (i1 + 4)