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Proof step 8 from proof INV-nextlevel (previous step)

b ∈ succ(c), reach(source, c, n), reachS(source, N, n + 1), ∃ m. m < n ∧ reach(source, c, m) ⊦ succ(c) = ∅, # succ(c) = 0, 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))), ∃ m0. ¬ n < m0 ∧ reach(source, b, m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
reach(source, c, m), m < n, reachS(source, N, n + 1), reach(source, c, n), b ∈ succ(c) ⊦ # succ(c) = 0, succ(c) = ∅, b ∈ V, ∃ m0. ¬ n < m0 ∧ reach(source, b, m0), ∃ 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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0])]]