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Proof step 20 from proof INV-step (previous step)

reachS(source, C, n), v ∈ C, b ∈ N ∪ (succ(v) \ V), b ∈ N → (∃ c. reach(source, c, n) ∧ b ∈ succ(c)) ∧ ¬ reach<(source, b, n + 1) ⊦ N ∪ (succ(v) \ V) = ∅, C = ∅, # C = 0, # (N ∪ (succ(v) \ V)) = 0, (∃ c. reach(source, c, n) ∧ b ∈ succ(c)) ∧ ¬ reach<(source, b, n + 1), ∃ 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 19:
b ∈ succ(v), v ∈ C, reachS(source, C, n) ⊦ succ(v) = ∅, # (N ∪ (succ(v) \ V)) = 0, # C = 0, C = ∅, N ∪ (succ(v) \ V) = ∅, # succ(v) = 0, b ∈ V, b ∈ N, ∃ 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)), (∃ c. reach(source, c, n) ∧ b ∈ succ(c)) ∧ ¬ reach<(source, b, n + 1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ s ≠ ∅ → # s ≠ 0], [CSIMPFORWARD : ⊦ a ∈ s → s ≠ ∅], [CSIMPSEQ : ⊦ s ∪ s0 = s0 ∪ s], [CSIMPSEQ : ⊦ (s ∪ s0) ∪ s1 = s ∪ s0 ∪ s1], [CSIMPSEQ : ⊦ a ∈ s1 \ s2 ↔ a ∈ s1 ∧ ¬ a ∈ s2], [CSIMPSEQ : ⊦ a ∈ s1 ∪ s2 ↔ a ∈ s1 ∨ a ∈ s2])]]