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

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