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Proof step 7 from proof inv-propagate (previous step)

rtc(n, a, b), Pelem(a), ∀ a, b. Pelem(a) ∧ p(a, b) → Pelem(b) ⊦ Pelem(b)

User applied rule structural induction

And obtained the following new goals

Proof step 8:
∀ a, b, Pelem. rtc(n0, a, b) ∧ Pelem(a) ∧ (∀ a, b. Pelem(a) ∧ p(a, b) → Pelem(b)) → Pelem(b), rtc(n0 +1, a, b), Pelem(a), ∀ a, b. Pelem(a) ∧ p(a, b) → Pelem(b) ⊦ Pelem(b)

Rule argument

indvar: n

Additional information

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