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Proof step 17 from proof reach-rec-rev (conclusion)

⊦ reach(a, b, n + 1) → (∃ c. c ∈ succ(a) ∧ reach(c, b, n))

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ reach(a, b, 1) ↔ b ∈ succ(a)
Proof step 2:
⊦ reach(a, b, 0) ↔ a = b
Proof step 16:
∀ a, b. reach(a, b, n0 + 1) → (∃ c. c ∈ succ(a) ∧ reach(c, b, n0)) ⊦ reach(a, b, n0 +1 + 1) → (∃ c. c ∈ succ(a) ∧ reach(c, b, n0 +1))

Rule argument

[VARWITHVARSEQSARG : n, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;])]]