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Proof step 5 from proof add-eq2pot-01 (previous step)

2 ^ i2 = i1 + 1, i + 1 = i2 + i0, 0 ≤ i0, 0 ≤ i, 0 ≤ j ⊦ 2 * 2 ^ i = 2 ^ i0 + j ↔ j = 2 ^ i0 * i1 ∧ 0 ≤ i2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 7:
0 ≤ i, 2 ^ i2 = i1 + 1, i + 1 = i2 + i0, 0 ≤ i0, 0 ≤ i, 0 ≤ j ⊦ 2 ^ (i + 1) = 2 ^ i0 + j ↔ j = 2 ^ i0 * i1 ∧ 0 ≤ i2

Rule argument

spec: int-pot inst: name: succ seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i, 2] flags: rewrite, current

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, 2