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Proof step 5 from proof ls-mult-2pot (previous step)

0 < j, 0 ≤ i1 + i, 0 ≤ i ⊦ j * 2 ^ i < 2 ^ (i1 + i) ↔ j < 2 ^ i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0
Proof step 7:
0 < j, 0 ≤ i, 0 ≤ i1 + i ⊦ j * 2 ^ i < 2 ^ (i1 + i) ↔ j < 2 ^ i1, 0 ≤ i1 ∧ 0 ≤ i
Proof step 14:
0 < j, 0 ≤ i1 + i, 0 ≤ i1, 0 ≤ i ⊦ j * 2 ^ i < 2 ^ i1 * 2 ^ i ↔ j < 2 ^ i1

Rule argument

spec: <toplevel> name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i, i1, 2] flags: <all paths>

Additional information

Used terms: i, i1, 2