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Proof step 4 from proof pot-dist-pos (previous step)

0 ≤ j, 0 ≤ j0, ∀ j1, j0, i. i→n(j1) < i→n(j) → 0 ≤ j1 ∧ 0 ≤ j0 → i ^ (j1 + j0) = i ^ j1 * i ^ j0 ⊦ i ^ (j + j0) = i ^ j * i ^ j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 6:
0 < j, 0 ≤ j, 0 ≤ j0, ∀ j1, j0, i. i→n(j1) < i→n(j) → 0 ≤ j1 ∧ 0 ≤ j0 → i ^ (j1 + j0) = i ^ j1 * i ^ j0 ⊦ i ^ (j + j0) = (i ^ j -1 * i) * i ^ j0

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i