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Proof step 26 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 + 4) ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 27:
0 < (3 + i1) * 6 + j0, j0 < 6, 1 + 6 * (3 + i1) + j0 ≤ 6 * (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) ⊦

Rule argument

fma: 8 * 2 ^ i1 ≤ 6 * (i1 + 4)

Additional information

Used simplifier rules: ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * 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% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i * (j + i0) < i * (j0 + i0) + j1 ↔ i * j < i * j0 + j1; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: 8 * 2 ^ i1 ≤ 6 * (i1 + 4)