reserve x, y for object, X, X1, X2 for set;

theorem Th3:
  R_Funcs(X) is Subset of R_PFuncs(X)
proof
  R_Funcs(X) c= R_PFuncs(X)
  proof
    let x be object;
    assume x in R_Funcs(X);
    then x is Function of X,REAL by Def13;
    hence thesis by Def12;
  end;
  hence thesis;
end;
