reserve X for non empty set;
reserve Y for ComplexLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);
reserve a,b for Complex;
reserve u,v,w for VECTOR of CLSStruct(#Funcs(X,the carrier of Y), (FuncZero(X,
    Y)),FuncAdd(X,Y),FuncExtMult(X,Y)#);

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;
