
theorem Th2:
for A,B be open_interval Subset of REAL st
 A meets B holds A \/ B is open_interval Subset of REAL
proof
    let A,B be open_interval Subset of REAL;
    assume A meets B; then
    A <> {} & B <> {} & A \/ B is interval by XBOOLE_1:65,XXREAL_2:89;
    hence A \/ B is open_interval Subset of REAL by Th1;
end;
