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Proof step 2 from proof INV-step (previous step)

b ∈ succ(v), reachS(source, N, n + 1), reachS(source, C, n), v ∈ C ⊦ succ(v) = ∅, # (V ∪ succ(v)) = 0, C = ∅, # C = 0, V ∪ succ(v) = ∅, # succ(v) = 0, reach<(source, b, n + 1), b ∈ V, ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ (a = v ∨ ¬ a ∈ C), ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N ∨ (∃ a. a ∈ C ∧ b1 ∈ succ(a) ∧ ¬ b1 ∈ V)), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ a ∈ C)), ∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ a ∈ C

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 9, [extquanttermlist: (v)abort:F, discard:F, computed:T]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ reachS(a, S, n) ∧ b ∈ S → (¬ reach(a, b, n) ↔ false)], [CSIMPSEQ : ⊦ b ∈ succ(a) ∧ reach<(source, a, n0) → ( ¬ reach<(source, b, n0 + 1) ↔ false)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (v)]]