reserve r,s,t,u for Real;

theorem Th36:
  for X being LinearTopSpace, V1,V2,V being Subset of X st V1+V2
  c= V holds Int V1 + Int V2 c= Int V
proof
  let X be LinearTopSpace, V1,V2,V be Subset of X such that
A1: V1+V2 c= V;
  Int V1 c= V1 & Int V2 c= V2 by TOPS_1:16;
  then Int V1 + Int V2 c= V1+V2 by Th11;
  then Int V1 + Int V2 c= V by A1;
  hence thesis by TOPS_1:24;
end;
