Up to definition of limsup as liminf computed on the reverse ordering.

Up to definition of limsup as liminf computed on the reverse ordering.
However, I am no longer sure that this is the best way to proceed since
the lemmas to be proved are a lot and the typing is difficult. However,
this work should be done anyway to state limsup f x = - liminf f (-x)
that we need anyway.