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Proof step 21 from proof int2bits-lslen-08 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
i→n(i + 2) + 1 < # int2bits(~(2 ^ i * 2 + 1)), 0 ≤ i, 2 ^ (2 + i) ≤ 2 ^ i * 2 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * 0 = 0;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ ~ j < ~ i ↔ i < j;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + ~ j = i - j;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;