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Proof step 29 from proof INV-step (previous step)

a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V, v ∈ C, reachS(source, C, n), reachS(source, N, n + 1), b0 ∈ succ(c), reach(source, c, n) ⊦ succ(c) = ∅, # C = 0, C = ∅, # succ(c) = 0, b0 ∈ succ(v) \ V, b0 ∈ N, reach<(source, b0, n + 1), ∃ a. a ≠ v ∧ a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V ∪ succ(v), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ a ∈ C)), c ≠ v ∧ c ∈ C ∧ ¬ b0 ∈ V ∪ succ(v)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
reach(source, c, n), b0 ∈ succ(c), reachS(source, N, n + 1), reachS(source, C, n), v ∈ C, b0 ∈ succ(a), a ∈ C ⊦ succ(a) = ∅, # succ(c) = 0, C = ∅, # C = 0, succ(c) = ∅, # succ(a) = 0, c ∈ C, b0 ∈ succ(v), b0 ∈ V, reach<(source, b0, n + 1), b0 ∈ N, ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ a ∈ C)), ∃ a0. a0 ∈ C ∧ b0 ∈ succ(a0)

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])]]