
theorem Th17:
  for X being non empty set holds for Y,Z being non empty Subset
of ExtREAL for F being Function of X,Y for G being Function of X,Z holds inf F
  + inf G <= inf(F + G)
proof
  let X be non empty set;
  let Y,Z be non empty Subset of ExtREAL;
  let F be Function of X,Y;
  let G be Function of X,Z;
A1: inf(rng F) + inf(rng G) <= inf(rng F + rng G) by Th8;
  inf(rng F + rng G) <= inf(F + G) by Th15,XXREAL_2:60;
  hence thesis by A1,XXREAL_0:2;
end;
