reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;
reserve V1,V2,V3 for Subset of V;

theorem
  V1 is linearly-closed implies for v,u being VECTOR of V st v in V1 & u
  in V1 holds v - u in V1
proof
  assume
A1: V1 is linearly-closed;
  let v,u be VECTOR of V;
  assume that
A2: v in V1 and
A3: u in V1;
  - u in V1 by A1,A3,Th21;
  hence thesis by A1,A2;
end;
