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Proof step 13 from proof int2bits-lelen (previous step)

i1 + 2 ≤ n→i(m), 0 ≤ i1 + 2, 0 ≤ i1 ∧ 2 ^ i1 ≤ i ∧ i < 2 ^ (i1 + 1), n→i(m) = i0 + 1, i < 2 ^ i1 * 2, 2 ^ i1 ≤ i, 0 ≤ i1, 0 < 2 ^ i1, 0 < i ⊦ ¬ 2 ^ i0 ≤ i, i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
n→i(m) = i0 + 1, 2 ^ i0 ≤ i, 0 < i, 0 < 2 ^ i1, 0 ≤ i1, 2 ^ i1 ≤ i, 2 ^ i0 < 2 ^ i1 * 2, i < 2 ^ i1 * 2, i1 < i0, 0 < i0 ⊦ i = 0

Rule argument

Additional information

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