reserve r, s, t, g for Real,

          r3, r1, r2, q3, p3 for Real;
reserve T for TopStruct,
  f for RealMap of T;
reserve p for Point of TOP-REAL 2,
  P for Subset of TOP-REAL 2,
  Z for non empty Subset of TOP-REAL 2,
  X for non empty compact Subset of TOP-REAL 2;

theorem Th22:
  for X being Subset of TOP-REAL 2, p being Point of TOP-REAL 2 st
  p in X holds (proj1|X).p = p`1
proof
  let X be Subset of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume p in X;
  hence (proj1|X).p = proj1.p by FUNCT_1:49
    .= p`1 by Def5;
end;
