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Proof step 34 from proof int2bits-lslen-08 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: int2bits-2pot-02: 0 ≤ i ⊦ int2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ ¬ m + n < m;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i * j = j * i;% ⊦ i < j → ¬ j < i;% ⊦ 0 ≤ j → 2 ^ j ≠ 0;% ⊦ 0 < i → (i < i * j ↔ 1 < j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i ∧ 0 ≤ j → abs(i + j) = abs(i) + abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ i + j < j ↔ i < 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i, j - 1