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Proof step 21 from proof pot2-est-div6 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 22:
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 ≤ 1 + 6 * (3 + i1) + 5 ⊦

Rule argument

fma: 1 + 6 * (3 + i1) + j0 ≤ 1 + 6 * (3 + i1) + 5

Additional information

Used simplifier rules: add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i * j + i = i * (j + 1); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * j0; (s)% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; (s) Used formulas: 1 + 6 * (3 + i1) + j0 ≤ 1 + 6 * (3 + i1) + 5