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Proof step 39 from proof INV-step (conclusion)

⊦ INV(C, N, V, n, source) ∧ v ∈ C → (¬ INV(C -- v, N ∪ (succ(v) \ V), V ∪ succ(v), n, 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 38:
reachS(source, N, n + 1), reachS(source, C, n), v ∈ C, ¬ (b ∈ V ∪ succ(v) ↔ reach<(source, b, n + 1) ∨ (∃ a. b ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ (a = v ∨ ¬ a ∈ C))) ∨ ¬ reachS(source, N ∪ (succ(v) \ V), n + 1) ∨ ¬ ( reach(source, c, n) ∧ b0 ∈ succ(c) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N ∪ (succ(v) \ V) ∨ (∃ a. a ≠ v ∧ a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V ∪ succ(v))) ⊦ C = ∅, # C = 0, ∃ b1. ¬ ((∃ c. reach(source, c, n) ∧ b1 ∈ succ(c)) ∧ ¬ reach<(source, b1, n + 1) → b1 ∈ N ∨ (∃ a. a ∈ C ∧ b1 ∈ succ(a) ∧ ¬ b1 ∈ V)), ∃ b1. ¬ (b1 ∈ V ↔ reach<(source, b1, n + 1) ∨ (∃ a. b1 ∈ succ(a) ∧ reach(source, a, n) ∧ ¬ reach<(source, a, n) ∧ ¬ a ∈ C))

Rule argument

[emptyarg]

Additional information

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