forall X, Y . subset(X, Y) ~ forall a . in(a, X) > in(a, Y).
forall X, Y . subset(X, Y) > subset(st(X), st(Y)).

forall X, M . subset(M, X) >
 . closed(M) ~ forall a . in(a, X) > . exists b (in(b, st(M)) & close(b, a)) > in(a, M).

forall X, M . subset(M, X) >
 . compact(M) ~ forall b . in(b, st(M)) > exists a . in(a, M) & close(b, a).

: forall X, M, F . subset(M, X) & compact(M) & subset(F, M) & closed(F) > compact(F).
