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I agree, it seems not very hard to be proved. It is a bit faraway from i was doing and it was better to include a reference than a proof. If you drop compactness the statemement does not hold. For instance if you take just a curve which lool likes the graph of $\sin (1/x)$ at both "ends" does not separate the plane. Also, if you don´t have the second part of the definition of pseudo-laminatios the statement does not hold (the stable manifold of a Smale´s horshoe does not separates the plane)
