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Proof step 3 from proof rtc-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b))
Proof step 5:
Pelem ^*(b, c), ∃ n. rtc(n, Pelem)(a, b) ⊦ Pelem ^*(a, c)

Rule argument

spec: <toplevel> name: rtc seq: ⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b)) subst: [b, a, Pelem] → [b, a, Pelem] flags: <all paths>

Additional information

Used terms: b, a, Pelem