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Proof step 26 from proof INV-step (previous step)

¬ reachS(source, N ∪ (succ(v) \ V), n + 1), reachS(source, N, n + 1), reachS(source, C, n), v ∈ C ⊦ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
v ∈ C, reachS(source, C, n), reachS(source, N, n + 1) ⊦ # C = 0, C = ∅, reachS(source, N ∪ (succ(v) \ V), n + 1), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ 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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]