Let $$A= (Q,Σ,δ,s,F)$$ be a NFA. Prove the following statement:
$∀q ∈ Q: (∃ w_2 ∈ Σ^* :δ (q, w_2) ∩ F \ne ∅ ⇒ ∃w_1 ∈ Σ^*:w_1w_2 ∈ L(A))$
I figured out that it means that if all the states have a path to the final state, that the word describing their path is a suffix of a word that is accepted from the NEA.
The thing is: How can I be sure that the NEA accepts all words with that suffix if it doesn't start from the s state.