Introduction to Lattice Theory.

there exists a -semi lattice structure which is strict and non empty, * there exists a -semi lattice structure which is strict and non empty, and * there exists a lattice structure which is strict and non empty.Let G be a non empty -semi lattice structure and let p, q be elements of G.The functor p q yields an element of G and is defined as follows:(Def. 1) p q = (the join operation of G)(p, q).Let G be a non empty -semi lattice structure and let p, q be elements of G.The functor p q yielding an element of G is defined as follows:(Def. 2) p q = (the meet operation of G) (p, q).Let G be a non empty -semi lattice structure and let p, q be elements of G.The predicate p q is defined as follows:(Def. 3) p q = q.