proposition: Lemma order_preserving_join_sl_mor: JoinSemiLattice_Morphism f.
proof: Proof. repeat (split; try apply _). intros x y. case (total (≤) x y); intros E. rewrite 2!join_r; try easy. now apply (order_preserving _). rewrite 2!join_l; try easy. now apply (order_preserving _). Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices