
theorem Th52:
  for P,Q,R being Point of TarskiEuclid2Space st between P,Q,R &
  Tn2TR P in inside_of_circle(0,0,1) & Tn2TR R in inside_of_circle(0,0,1)
  holds Tn2TR Q in inside_of_circle(0,0,1)
  proof
    let P,Q,R be Point of TarskiEuclid2Space;
    assume that
A1: between P,Q,R and
A2: Tn2TR P in inside_of_circle(0,0,1) & Tn2TR R in inside_of_circle(0,0,1);
    LSeg(Tn2TR P,Tn2TR R) c= inside_of_circle(0,0,1) by A2,RLTOPSP1:22;
    hence thesis by A1,GTARSKI2:20;
  end;
