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Proof step 23 from proof int2bits-len-range (previous step)

i→n(i) + 1 < # int2bits(~(j + 1)), 0 < 2 ^ i0, j < 0, 2 ^ i0 + j ≤ i0, i0 ≤ i, j < i0, 0 < 2 ^ i, j + 1 < 2 ^ i0, 2 ^ i0 + j < 2 ^ i, 0 ≤ i, 2 ^ i0 + j ≤ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, j < 2 ^ i0, 0 < 2 ^ i0 * 2 + j, 2 ^ i0 + j ≤ 0, 0 ≤ i0, 0 ≤ 2 ^ i + j ⊦ j = ~(2 ^ i0), j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
0 < i, j < ~1, (2 ^ i0 + j) + 1 < 2 ^ i, 1 < 2 ^ i0, 2 ^ i0 + j < i0, i0 < i, 2 ^ i0 + j < i, 0 ≤ i0, 0 ≤ 2 ^ i + j, i→n(i) + 1 < # int2bits(~(j + 1)), 2 ^ i0 + j ≤ i0, i0 ≤ i, j < i0, 0 < 2 ^ i, j + 1 < 2 ^ i0, 2 ^ i0 + j < 2 ^ i, 0 ≤ i, 2 ^ i0 + j ≤ i, j < 2 ^ i, j < i, j < 2 ^ i0, 0 < 2 ^ i0 * 2 + j, 2 ^ i0 + j < 0, j < 0, 0 ≤ 2 ^ i0, 0 < 2 ^ i0, (2 ^ i0 + j) + 1 < i ⊦ j = 0, 2 ^ i0 + j = 0

Rule argument

Additional information

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