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Proof step 36 from proof INV-nextlevel (previous step)

reach(source, c, m), b0 ∈ succ(c), c ∈ succ(c0), reach(source, c0, n), reach(source, b0, 2 + n), reachS(source, N, n + 1), m ≤ n ⊦ succ(c) = ∅, succ(c0) = ∅, # succ(c) = 0, # succ(c0) = 0, ∃ m. m < 2 + n ∧ reach(source, b0, m), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n))), ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N), ∃ a. a ∈ N ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V, c ∈ N ∧ ¬ b0 ∈ V

User applied rule exists right

And obtained the following new goals

Proof step 35:
reach(source, c, m), b0 ∈ succ(c), c ∈ succ(c0), reach(source, c0, n), reach(source, b0, 2 + n), reachS(source, N, n + 1), m ≤ n ⊦ succ(c) = ∅, succ(c0) = ∅, # succ(c) = 0, # succ(c0) = 0, m + 1 < 2 + n ∧ reach(source, b0, m + 1), ∃ m. m < 2 + n ∧ reach(source, b0, m), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n))), ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N), ∃ a. a ∈ N ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V, c ∈ N ∧ ¬ b0 ∈ V

Rule argument

[EXRARG : pos: right 5, [extquanttermlist: (m + 1)abort:F, discard:F, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m + 1)]]