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Proof step 10 from proof int2bits-len-range (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 11:
0 ≤ i, 2 ^ i ≤ j, j < 2 ^ (i + 1) ⊦ # int2bits(j) = i→n(i + 2)
Proof step 12:
# int2bits(j) = i→n(i0 + 2), 0 ≤ 2 ^ i + j, j < 2 ^ i, 0 ≤ i0, 2 ^ i0 ≤ j, j < 2 ^ i0 * 2, 1 < 2 ^ i, 0 < i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 < j, i0 < i, 0 < 2 ^ i0, i→n(i) + 1 < # int2bits(j) ⊦

Rule argument

name: int2bits-len-pos subst: [i, j] → [i0, j]

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 ↔ j ≤ i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i0, j