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Proof step 11 from proof le-2pot-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 ≤ j0, j0 < 2, 0 ≤ i, 0 ≤ i0, i0 * 2 + j0 ≤ 2 ^ i * 2 + 1, 2 ^ i < i0 ⊦

Rule argument

Additional information

Used simplifier rules: succ: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; 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