Completely free lattices generated by partially ordered sets
Richard A. Dean · Transactions of the American Mathematical Society · 1956
Lemma 3. The relation (S) on the words on the pi is reflexive and transitive.Proof.Part I.A S4.The proof is by induction on \(A).For \(A) =1, A =pt and the result follows from that property for the set P. Assume therefore that the result is verified when \(A) \C2 by (2.4).Case 1.2.B=pit A=Ai\JA2.