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Proof step 2 from proof rtc-trans (previous step)

Pelem ^*(a, b), Pelem ^*(b, c) ⊦ Pelem ^*(a, c)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b))
Proof step 4:
∃ n. rtc(n, Pelem)(a, b), Pelem ^*(b, c) ⊦ Pelem ^*(a, c)

Rule argument

spec: inst: name: rtc seq: ⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b)) subst: [b, a, Pelem] → [b, a, Pelem] flags: rewrite, current

Additional information

Used terms: b, a, Pelem