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

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