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Proof step 4 from proof pot-div (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i);%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j0, i0, i