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Proof step 7 from proof pot-dist-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 9:
0 < j + j0, 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)-1 * i = (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 + j0, i] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j + j0, i