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Proof step 31 from proof pot2-est-div6 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
0 < (3 + i1) * 6 + j0, 2 ^ i1 < i1 + 4, 0 ≤ i1, 4 * 2 ^ i1 ≤ 3 * (4 + i1), 8 * 2 ^ i1 ≤ (3 + i1) * 6 + j0 + 1, 36 ≤ (3 + i1) * 6 + j0, 0 ≤ j0, 8 * 2 ^ i1 ≤ 6 * (i1 + 4), j0 ≤ 5 ⊦

Rule argument

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); (s)%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)% ⊦ (* i1) * j < (* i2) * j ↔ 0 < (i2 - i1) * j; (s)% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * j0; (s)