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Proof step 40 from proof int2int-neg (previous step)

~2 * 2 ^ i + 1 < i, ~2 * 2 ^ i < i, ~2 * 2 ^ i < i + 2, j < ~1, j + 2 ^ i < i, j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, ~2 * 2 ^ i ≤ j, ~2 * 2 ^ i < j, j + 2 ^ i < 0, ~2 * 2 ^ i ≤ i, ~2 * 2 ^ i ≤ i + 2, 0 ≤ 2 ^ i, 0 < 2 ^ i, j < 0, ~2 * 2 ^ i < ~1, 1 < 2 ^ i ⊦ 3 * 2 ^ i + j = 0, 4 * 2 ^ i = 2 ^ (2 + i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i, 2, 2] rotate: F spec: int-pot inst: name: pot-dist-pos

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 2, 2