
theorem
for A be Interval, B,C be open_interval Subset of REAL
 st A c= B \/ C & A meets B & A meets C holds B meets C
proof
    let A be Interval, B,C be open_interval Subset of REAL;
    assume A1: A c= B \/ C & A meets B & A meets C;
    A is open_interval or A is closed_interval or
    A is right_open_interval or A is left_open_interval
      by MEASURE5:1;
    hence thesis by A1,Lm1,Lm2,Lm3,Lm4;
end;
