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Proof step 1 from proof add-eq2pot-01 (conclusion)

⊦ 0 ≤ j ∧ 0 ≤ i ∧ 0 ≤ i0 → (2 * 2 ^ i = 2 ^ i0 + j ↔ j = 2 ^ i0 * (2 ^ (i + 1 - i0) - 1) ∧ i0 ≤ i + 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ j, 0 ≤ i, 0 ≤ i0 ⊦ 2 * 2 ^ i = 2 ^ i0 + j ↔ j = 2 ^ i0 * (2 ^ (i + 1 - i0) - 1) ∧ i0 ≤ i + 1

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs