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Proof step 8 from proof grz (previous step)

0 < i ^ j, 0 < i, j < 0 ⊦ i ^ ~ j = 1, i = 1, 0 ≤ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i < 0 → j ^ i = 1 / j ^ abs(i)

Rule argument

spec: <toplevel> name: Pot-neg seq: ⊦ i < 0 → j ^ i = 1 / j ^ abs(i) subst: [i, j] → [j, i] flags: <all paths>

Additional information

Used simplifier rules: zero-02: ⊦ j < 0 → (i ^ ~ j = 0 ↔ i = 0);%zero-03: ⊦ j < 0 → 0 ^ ~ j = 0;% ⊦ i < 0 → abs(i) = ~ i; (s)%j ≠ 0 ⊦ 0 < 1 / j ↔ j = 1; (s) Used terms: j, i