Victor, a kind of followup: https://trac.sagemath.org/ticket/24584
I think we should add is_extension() to posets, and then maybe functions to list "minimal extensions" and "minimal un-extensions" (right term for that?) of a poset. I think that the last one is just a way to remove a covering relation. With those we could have principal upper and lower sets of a power poset, i.e. an extensions poset you asked.
-- Jori Mäntysalo
