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Proof step 13 from proof rtc-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ Pelem ^*(a, b) ↔ (∃ n. rtc(n, Pelem)(a, b))
Proof step 15:
Pelem(a, c0), Pelem ^*(b, c), rtc(n0, Pelem)(c0, b), rtc(n, Pelem)(c0, c) ⊦ ∃ n. rtc(n, Pelem)(a, c)

Rule argument

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

Additional information

Used terms: c, a, Pelem