theorem Th10:
  F \/ G on L iff F on L & G on L
proof
  thus F \/ G on L implies F on L & G on L by Th6,XBOOLE_1:7;
  assume
A1: F on L & G on L;
  let C be POINT of S;
  assume C in F \/ G;
  then C in F or C in G by XBOOLE_0:def 3;
  hence thesis by A1;
end;
