let A be Subset of (TOP-REAL 2); for p1, p2, q1, q2 being Point of (TOP-REAL 2) holds Segment A,p1,p2,q1,q2 c= A
let p1, p2, q1, q2 be Point of (TOP-REAL 2); Segment A,p1,p2,q1,q2 c= A
Segment A,p1,p2,q1,q2 = (R_Segment A,p1,p2,q1) /\ (L_Segment A,p1,p2,q2)
by JORDAN6:def 5;
then
( R_Segment A,p1,p2,q1 c= A & Segment A,p1,p2,q1,q2 c= R_Segment A,p1,p2,q1 )
by JORDAN6:21, XBOOLE_1:17;
hence
Segment A,p1,p2,q1,q2 c= A
by XBOOLE_1:1; verum