reserve f for non constant standard special_circular_sequence,
  i,j,k,i1,i2,j1,j2 for Nat,
  r,s,r1,s1,r2,s2 for Real,
  p,q for Point of TOP-REAL 2,
  G for Go-board;

theorem Th5: :: ouogolnic !!!
  for P,Q being convex Subset of TOP-REAL 2 holds P /\ Q is convex
proof
  let P,Q be convex Subset of TOP-REAL 2;
  let p,q;
  assume that
A1: p in P /\ Q and
A2: q in P /\ Q;
A3: p in P by A1,XBOOLE_0:def 4;
  q in P by A2,XBOOLE_0:def 4;
  then
A4: LSeg(p,q) c= P by A3,JORDAN1:def 1;
A5: p in Q by A1,XBOOLE_0:def 4;
  q in Q by A2,XBOOLE_0:def 4;
  then LSeg(p,q) c= Q by A5,JORDAN1:def 1;
  hence thesis by A4,XBOOLE_1:19;
end;
