reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;
reserve X,X1,X2 for Subset of A;
reserve Y for Subset of B;
reserve R,R1,R2 for Subset of [:A,B:];
reserve FR for Subset-Family of [:A,B:];
reserve R for Relation of A,B;
reserve S for Relation of B,C;

theorem :: (13.2)
  proj2 (R*S) = S.:(proj2 R) & proj2 (R*S) c= proj2 S
proof
  thus
A1: proj2 (R*S) = (R*S).:A by Th50
    .= S.:(R.:A) by RELAT_1:126
    .= S.:(proj2 R) by Th50;
  proj2 R = rng R;
  then S.:(proj2 R) c= S.:B by RELAT_1:123;
  hence thesis by A1,Th50;
end;
