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Proof step 5 from proof rtc-trans (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 6:
∀ Pelem, a, b, c. rtc(n0, Pelem)(a, b) ∧ Pelem ^*(b, c) → Pelem ^*(a, c), rtc(n0 +1, Pelem)(a, b), Pelem ^*(b, c) ⊦ Pelem ^*(a, c)

Rule argument

indvar: n

Additional information

Used simplifier rules: rtc-base: ⊦ rtc(0, Pelem)(a, b) ↔ a = b;%nat freely generated by 0, +1;;