Is the "rocket" pattern inversible?

Question

The rocket pattern in slitherlink is when a 3 sees a 1 in a diagonal, with two crosses (the exhaust) on the opposite side.

    3
x 1
  x

two lines can be added adjacent to the 3 and opposite to the 1, making the top of the rocket.

    _
    3|
x 1
  x

I used the reverse pattern several times, but I cannot prove that it is true or just a coincidence.

    _                     _ 
    3|                    3|
  1           ====>   x 1
                        x
   
   

Is there a proof that the "reverse rocket" is a valid pattern?

Answer 1

The vertex (I'll call it V) shared between the 3 and 1 has four possible edges leading out: two which are along the 3 and two along the 1. Since the 3 already is using its two non-V edges, exactly one of its V edges must be used. Since the loop can't have a hanging edge, another of V's edges must also be used. The only possibilities are V's edges along the 1. Since one of these is used the 1 is at its limit of edges used, and it cannot use either of its non-V edges. Q.E.D.