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Proof step 13 from proof int2bits-lslen-08 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 15:
¬(0 ≤ i ∧ ~(2 ^ (i + 1)) ≤ j - 1 ∧ j - 1 < ~(2 ^ i)), i→n(i + 2) + 1 < # int2bits(j - 1), j < 0, j + 2 ^ i < 0, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j ⊦

Rule argument

name: int2bits-len-neg rotate: F subst: [i, j] → [i, j - 1]

Additional information

Used simplifier rules: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + ~ j = i - j;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i, j - 1