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Proof step 14 from proof cast-b2i-01 (previous step)

0 ≤ i0, 0 < i0, 7 ≤ i0, 2 ^ i0 < b2i(by) + 1, 2 ^ i0 < 128 ⊦ ~1 = i0, cast(i0 + 1, b2i(by)) = b2i(by)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
2 ^ i0 < 128, 0 ≤ i0, 0 < i0, 7 ≤ i0, 2 ^ i0 ≤ b2i(by) ⊦ ~1 = i0, cast(i0 + 1, b2i(by)) = b2i(by)

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j + 1 ↔ i ≤ j;