Section UPPER_SEMILATTICE.
Context {D : Type} {PROSET : isProset D} {UPPER_SEMILATTICE : isUpperSemilattice D (PROSET := PROSET)}.

Lemma join_lattice_le_intro (x1 : D) (x2 : D)
: forall x : D, x1 =< x -> x2 =< x -> join_lattice x1 x2 =< x.