reserve i, i1, i2, j, j1, j2, k, m, n, t for Nat,
  D for non empty Subset of TOP-REAL 2,
  E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p, q, x for Point of TOP-REAL 2,
  r, s for Real;

theorem :: Uogolnic i przenisc !!!
  for A,B being Subset of TOP-REAL 2 st A meets B holds proj2.:A meets proj2.:B
proof
  let A,B be Subset of TOP-REAL 2;
  assume A meets B;
  then consider e being object such that
A1: e in A and
A2: e in B by XBOOLE_0:3;
  reconsider e as Point of TOP-REAL 2 by A1;
  e`2 = proj2.e by PSCOMP_1:def 6;
  then e`2 in proj2.:A & e`2 in proj2.:B by A1,A2,FUNCT_2:35;
  hence thesis by XBOOLE_0:3;
end;
