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Proof step 4 from proof INVR-nextlevel (previous step)

n1 = m + 1, reach(source, dest, n1 + n), reachS(source, N, n + 1), reach(b, dest, m), b ∈ N, ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, m) ∨ reach<(a, dest, m) ⊦ N = ∅, # N = 0, n1 = 0, reach<(b, dest, m), reach<(source, dest, n1 + n), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a. b0 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
dest ∈ succ(c), reach(source, c, m + n), b ∈ N, reach(b, dest, m), reachS(source, N, n + 1), ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, m) ∨ reach<(a, dest, m) ⊦ succ(c) = ∅, # N = 0, N = ∅, # succ(c) = 0, reach<(source, dest, (m + 1) + n), reach<(b, dest, m), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a. b0 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n))), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ s ≠ ∅ → # s ≠ 0], [CSIMPFORWARD : ⊦ a ∈ s → s ≠ ∅], [CSIMPSEQ : ⊦ reach(a, b, n + 1) ↔ (∃ c. reach(a, c, n) ∧ b ∈ succ(c))], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0])]]