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Proof step 25 from proof rtc+-unfold-last (previous step)

rtc(n, a, c), p(c, b) ⊦ ∃ c. p(a, c) ∧ rtc(n, c, b)

User applied rule structural induction

And obtained the following new goals

Proof step 26:
∀ a, c, b. rtc(n0, a, c) ∧ p(c, b) → (∃ c. p(a, c) ∧ rtc(n0, c, b)), rtc(n0 +1, a, c), p(c, b) ⊦ ∃ c. p(a, c) ∧ rtc(n0 +1, c, b)

Rule argument

indvar: n

Additional information

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