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Proof step 21 from proof int2bits-lslen-07 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
0 ≤ i, 2 ^ i ≤ j, j < 2 ^ (i + 1) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 23:
0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1), 0 ≤ i, 0 < j, j < 2 ^ i * 2, 2 ^ i ≤ j, i→n(i + 2) + 1 < # int2bits(j + 1) ⊦ 0 = j

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i, j