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Proof step 27 from proof cast-mod-neg-low (previous step)

0 < j + 2 ^ i, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0, 0 < i, i→n(i) ≤ # int2bits(j) ⊦ # int2bits(j) = i→n(i) + 1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i + 2 ^ i, j = ~1, i = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

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