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Proof step 38 from proof INV-step (previous step)

reachS(source, N, n + 1), reachS(source, C, n), v ∈ C, ¬ (b ∈ V ∪ succ(v) ↔ reach<(source, b, n + 1) ∨ (∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ (a = v ∨ ¬ a ∈ C))) ∨ ¬ reachS(source, N ∪ (succ(v) \ V), n + 1) ∨ ¬ ( reach(source, c, n) ∧ b0 ∈ succ(c) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N ∪ (succ(v) \ V) ∨ (∃ a. a ≠ v ∧ a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V ∪ succ(v))) ⊦ C = ∅, # C = 0, ∃ 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))

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: left 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]