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Proof step 23 from proof INV-nextlevel (previous step)

b ∈ succ(a) ∧ reach(source, c, n) ∧ a ∈ succ(c) ∧ ¬ reach<(source, a, n + 1) ∧ ¬ a ∈ N, reachS(source, N, n + 1) ⊦ b ∈ V, reach<(source, b, n + 1), ∃ 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. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
reachS(source, N, n + 1), a ∈ succ(c), reach(source, c, n), b ∈ succ(a) ⊦ succ(c) = ∅, succ(a) = ∅, # succ(c) = 0, # succ(a) = 0, reach<(source, a, n + 1), a ∈ N, reach<(source, b, n + 1), b ∈ V, ∃ a. b ∈ 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), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ s ≠ ∅ → # s ≠ 0], [CSIMPFORWARD : ⊦ a ∈ s → s ≠ ∅])]]