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Proof step 49 from proof INV-nextlevel (previous step)

reach(source, b0, (n + 1) + 1) ↔ (∃ c. reach(source, c, n + 1) ∧ b0 ∈ succ(c)), reachS(source, N, n + 1), reach(source, b0, 2 + n) ⊦ reach<(source, b0, 2 + n), ∃ a. a ∈ N ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V, ∃ 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)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
b0 ∈ succ(c), c ∈ succ(c0), reach(source, c0, n), reach(source, b0, 2 + n), reachS(source, N, n + 1) ⊦ succ(c) = ∅, succ(c0) = ∅, # succ(c) = 0, # succ(c0) = 0, reach<(source, b0, 2 + n), ∃ 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. a ∈ N ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V

Rule argument

[emptyarg]

Additional information

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