reserve P,P1,P2,R for Subset of TOP-REAL 2,
  p,p1,p2,p3,p11,p22,q,q1,q2,q3,q4 for Point of TOP-REAL 2,
  f,h for FinSequence of TOP-REAL 2,
  r for Real,
  u for Point of Euclid 2,
  n,m,i,j,k for Nat,
  x,y for set;
reserve P, R for Subset of TOP-REAL 2;

theorem
  R is being_Region & p in R & P={q: q=p or ex P1 being Subset of
  TOP-REAL 2 st P1 is_S-P_arc_joining p,q & P1 c=R} implies R = P
by Th27,Th26;
