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Proof step 9 from proof pot2-est-div6 (previous step)

i0 = i1 + 1, j0 < 6, 2 ^ i1 ≤ 3 * (i0 + 1), 0 < i0 * 6 + j0, 0 ≤ i0, 0 ≤ j0, 36 ≤ i0 * 6 + j0, 2 ^ i1 * 2 ≤ (i0 * 6 + j0) + 1, 0 < i0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 ≤ i1, 0 < (i1 + 1) * 6 + j0, 2 ^ i1 * 2 ≤ ((i1 + 1) * 6 + j0) + 1, 36 ≤ (i1 + 1) * 6 + j0, 0 ≤ j0, 2 ^ i1 ≤ 3 * (2 + i1), j0 < 6 ⊦

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2