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Proof step 53 from proof int2int-neg (previous step)

0 ≤ 2 ^ i + 2 ^ i, 0 < i + 2 ^ i, 0 ≤ 2 ^ i + i, 1 < 2 ^ i + 2 ^ i, ~2 ≤ 2 ^ i + i, ~2 < i + 2 ^ i, ~2 < i, 0 ≤ 2 ^ i, 0 ≤ i, ~2 ≤ i, 0 < 2 ^ i ⊦ 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;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 2, 2