
theorem
for X be non empty set, f1,f2 be Function of X,ExtREAL
 st f1 is without-infty without+infty holds
  f1-f2 is Function of X,ExtREAL
& for x be Element of X holds (f1-f2).x = f1.x - f2.x
proof
   let X be non empty set, f1,f2 be Function of X,ExtREAL;
   assume A1: f1 is without-infty without+infty;
   dom f1 = X & dom f2 = X by FUNCT_2:def 1; then
A2:dom(f1-f2) = X /\ X by A1,Th23;
   hence f1-f2 is Function of X,ExtREAL by FUNCT_2:def 1;
   thus thesis by A2,MESFUNC1:def 4;
end;
