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Proof step 7 from proof uint2bits-len-max (previous step)

0 ≤ i0 ∧ 2 ^ i0 ≤ j ∧ j < 2 ^ (i0 + 1), 0 < j, j < 2 ^ i, i→n(i) + 1 < i→n(i0 + 2), j < 2 ^ (i0 + 1), 2 ^ i0 ≤ j, 0 ≤ i0, 0 ≤ i, 1 < 2 ^ i, 1 < 2 ^ (i0 + 1), i0 < i, 0 < i, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ (i0 + 1), 0 ≤ 2 ^ (i0 + 1) ⊦ 0 = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ 2 ^ (i0 + 1), 0 < 2 ^ (i0 + 1), 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 < i, i0 < i, 1 < 2 ^ (i0 + 1), 1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 2 ^ i0 ≤ j, j < 2 ^ (i0 + 1), i→n(i) + 1 < i→n(i0 + 2), j < 2 ^ i, 0 < j ⊦ 0 = j, ~2 = i0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)