theorem Th7:
  (FuncExtMult(X,Y)).[1r,f] = f
proof
  now
    let x be Element of X;
    thus ((FuncExtMult(X,Y)).[1r,f]).x = 1r*(f.x) by Th2
      .= f.x by CLVECT_1:def 5;
  end;
  hence thesis by FUNCT_2:63;
end;
