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Proof step 19 from proof cast-b2i-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
2 ^ i0 + b2i(by) < 0, 0 ≤ i0, 0 < i0, 7 ≤ i0 ⊦ ~1 = i0, cast(i0 + 1, b2i(by)) = b2i(by)

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)