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Proof step 46 from proof int2bits-add-high (previous step)

j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 2 ^ i0 ≤ 2 ^ (1 + i0), 0 ≤ j0 + 2 ^ i, 2 ^ i0 ≤ 2 ^ (2 + i0), 0 < i0, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 ≤ 2 ^ i * (2 ^ (1 + i0) + 1 - 2 ^ i0) + j0 ⊦ true ' + mklist(false, i→n(i0)) = sgn(uint2bits(2 ^ (2 + i0) - 2 ^ i0).rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0
Proof step 48:
0 ≤ 2 ∧ 0 ≤ i0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 2 ^ i0 ≤ 2 ^ (1 + i0), 0 ≤ j0 + 2 ^ i, 2 ^ i0 ≤ 2 ^ 2 * 2 ^ i0, 0 < i0, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 ≤ 2 ^ i * (2 ^ (1 + i0) + 1 - 2 ^ i0) + j0 ⊦ true ' + mklist(false, i→n(i0)) = sgn(uint2bits(2 ^ 2 * 2 ^ i0 - 2 ^ i0).rest)

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i0, 2, 2] rotate: F spec: int-pot inst: name: pot-dist-pos

Additional information

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