Prove or give a counterexample:

The predicate can$$share$(\backslash$alpha $,$ x$,$ y$,$ G$0)$ is true if and only if there is an edge from x to y in G$0$ labeled $\backslash$alpha $,$ or if the following hold simultaneously.

There is a vertex s with an s$-$to$-$y edge labeled $\backslash$alpha $.$

There is a subject vertex x$$ such that x$=$ x or x$$ initially spans to x$.$

There is a subject vertex s$$ such that s$=$ s or s$$ initially spans to s$.$

There is a sequence of subjects x$1,...,$ xn with x$1=$ x$,$ xn $=$ s$,$ and xi and xi$+1(1<=$ i $<$ n$)$ being connected by an edge labeled t$,$ an edge labeled g$,$ or a bridge.