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Proof step 8 from proof le-2pot (previous step)

0 < i + 1, 0 ≤ j0, j0 < 2, 2 ^ i ≤ i0, 0 ≤ i, 0 ≤ i0 ⊦ 2 ^ (i + 1)-1 * 2 ≤ i0 * 2 + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 ≤ j0, j0 < 2, 2 ^ i ≤ i0, 0 ≤ i0, 0 ≤ i ⊦ 2 ^ i * 2 ≤ i0 * 2 + j0

Rule argument

Additional information

Used simplifier rules: pred: ⊦ (i + 1)-1 = i; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs