reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  R"(X /\ Y) c= R"X /\ R"Y
proof
  let x be object;
  assume x in R"(X /\ Y);
  then consider y such that
A1: [x,y] in R and
A2: y in X /\ Y by Def12;
  y in Y by A2,XBOOLE_0:def 4;
  then
A3: x in R"Y by A1,Def12;
  y in X by A2,XBOOLE_0:def 4;
  then x in R"X by A1,Def12;
  hence thesis by A3,XBOOLE_0:def 4;
end;
