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Proof step 5 from proof pot-div (previous step)

0 < i, 0 ≤ j0, 0 ≤ i0 + j0, 0 ≤ i0 ⊦ i ^ (i0 + j0) / i ^ j0 = i ^ i0

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 < i, 0 ≤ i0 + j0, 0 ≤ i0, 0 ≤ j0 ⊦ (i ^ i0 * i ^ j0) / i ^ j0 = i ^ i0

Rule argument

spec: <toplevel> name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [j0, i0, i] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: j0, i0, i