theorem Th17:
  X0 is SubSpace of X1 implies X0 meets X1 & X1 meets X0
proof
  assume X0 is SubSpace of X1; then
A1: (the carrier of X0) meets (the carrier of X1) by XBOOLE_1:28,TSEP_1:4;
  hence X0 meets X1 by TSEP_1:def 3;
  thus thesis by A1,TSEP_1:def 3;
end;
