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Proof step 53 from proof INV-nextlevel (conclusion)

⊦ INV(∅, N, V, n, source) → (¬ INV(N, ∅, V, n + 1, source) ↔ false)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ INV(C, N, V, n, source) ↔ ¬ ¬ ( (∀ b. b ∈ V ↔ reach<(source, b, n + 1) ∨ (∃ a. b ∈ succ(a) ∧ reachS(source, {a} , n) ∧ ¬ a ∈ C)) ∧ reachS(source, C, n) ∧ reachS(source, N, n + 1) ∧ (∀ b. reachS(source, {b} , n + 1) → b ∈ N ∨ (∃ a. a ∈ C ∧ b ∈ succ(a) ∧ ¬ b ∈ V)))
Proof step 52:
reachS(source, N, n + 1), ¬ (b ∈ V ↔ reach<(source, b, 2 + n) ∨ (∃ a. b ∈ succ(a) ∧ (∃ c. reach(source, c, n) ∧ a ∈ succ(c)) ∧ ¬ reach<(source, a, n + 1) ∧ ¬ a ∈ N)) ∨ ¬ (reach(source, b0, 2 + n) ∧ ¬ reach<(source, b0, 2 + n) → (∃ a. a ∈ N ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V)) ⊦ ∃ 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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ a ∈ ∅], [CSIMPSEQ : ⊦ reachS(a, ∅, n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ reach(a, b, n + 1) ↔ (∃ c. reach(a, c, n) ∧ b ∈ succ(c))], [CSIMPSEQ : ⊦ reachS(a, ∅ ++ b, n) ↔ ¬ ¬ ( reach(a, b, n) ∧ ¬ reach<(a, b, n))], [CSIMPSEQ : ⊦ {a} = ∅ ++ a], [CSIMPSEQ : ⊦ m + n = n + m])]]