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Proof step 9 from proof rtc-trans (previous step)

Pelem ^*(b, c), Pelem(a, c0), rtc(n0, Pelem)(c0, b), Pelem ^*(c0, c) ⊦ Pelem ^*(a, c)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b))
Proof step 11:
Pelem ^*(b, c), Pelem(a, c0), rtc(n0, Pelem)(c0, b), ∃ n. rtc(n, Pelem)(c0, c) ⊦ Pelem ^*(a, c)

Rule argument

spec: inst: name: rtc seq: ⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b)) subst: [b, a, Pelem] → [c, c0, Pelem] flags: rewrite, current

Additional information

Used terms: c, c0, Pelem