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Proof step 32 from proof BFS-returns-fail-implies-not-reachable (previous step)

dest ∈ S0, (∀ b. b ∈ S1 ↔ reach<(source, b, n0 + 1) ∨ (∃ a. b ∈ succ(a) ∧ reachS(source, {a} , n0) ∧ ¬ a ∈ S0)) ∧ reachS(source, S0, n0) ∧ reachS(source, S, n0 + 1) ∧ (∀ b. reachS(source, {b} , n0 + 1) → b ∈ S ∨ (∃ a. a ∈ S0 ∧ b ∈ succ(a) ∧ ¬ b ∈ S1)), ∀ n. ¬ reach(source, dest, n) ⊦ S0 = ∅, # S0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
dest ∈ S0, reachS(source, S0, n0), reachS(source, S, n0 + 1), ∀ n. ¬ reach(source, dest, n), ∀ b. b ∈ S1 ↔ reach<(source, b, n0 + 1) ∨ (∃ a. b ∈ succ(a) ∧ reachS(source, ∅ ++ a, n0) ∧ ¬ a ∈ S0), ∀ b. reachS(source, ∅ ++ b, n0 + 1) → b ∈ S ∨ (∃ a. a ∈ S0 ∧ b ∈ succ(a) ∧ ¬ b ∈ S1) ⊦ S0 = ∅, # S0 = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ {a} = ∅ ++ a])]]