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Proof step 6 from proof INVR-nextlevel (previous step)

n0 = n1 + n ∧ n ≤ n0, reachS(source, N, n + 1), reach(b, dest, n1 - 1), b ∈ N, n < n0, reach(source, dest, n0), ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, n0 - n + 1) ∨ reach<(a, dest, n0 - n + 1) ⊦ N = ∅, # N = 0, reach<(b, dest, n1 - 1), reach<(source, dest, n0), ∃ 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 5:
reach(source, dest, n1 + n), reachS(source, N, n + 1), reach(b, dest, n1 - 1), b ∈ N, ∀ a. ¬ a ∈ N ∨ ¬ reach(a, dest, n1 - 1) ∨ reach<(a, dest, n1 - 1) ⊦ N = ∅, # N = 0, n1 = 0, reach<(b, dest, n1 - 1), 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)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n - n + n1 = m - n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPSEQ : ⊦ m < n → m ≤ n])]]