reserve x,y for set;
reserve s,r for Real;
reserve r1,r2 for Real;
reserve n for Nat;
reserve p,q,q1,q2 for Point of TOP-REAL 2;
reserve C for Simple_closed_curve;

theorem
  Upper_Middle_Point C in C
proof
A1: Upper_Middle_Point C in Upper_Arc C by Th67;
  Upper_Arc C c= C by Th61;
  hence thesis by A1;
end;
