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Proof step 66 from proof cast-mod-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 2 ^ i ≤ j, j < 2 ^ (i + 1) ⊦ # int2bits(j) = i→n(i + 2) subst: [i, j] → [i - 1, j % 2 ^ i] rotate: F spec: int2bits inst: name: int2bits-len-pos

Additional information

Used simplifier rules: ⊦ 0 < i → ¬ 2 ^ i ≤ j % 2 ^ i;% ⊦ i + (j - i) = j;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + (j - i0) = i + j - i0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ i + 0 = i; Used terms: i - 1, j % 2 ^ i