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Proof step 9 from proof le-2pot-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
j0 < 2, i0 ≤ 2 ^ i, 0 ≤ j0, 0 ≤ i0, 0 ≤ 2 ^ i, 0 ≤ i ⊦ i0 * 2 + j0 ≤ 2 ^ i * 2 + 1

Rule argument

Additional information

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