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Proof step 8 from proof int2bits-lslen-07 (previous step)

0 ≤ i ∧ ~(2 ^ (i + 1)) ≤ j ∧ j < ~(2 ^ i), i→n(i + 2) + 1 < # int2bits(j + 1), ~1 ≤ i, j < 0, j + 2 ^ i < 0, 0 ≤ 2 ^ (i + 1) + j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i→n(i + 2) + 1 < # int2bits(j + 1), j < 0, j + 2 ^ i < 0, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i * j = j * i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;