reserve n for Nat;

theorem :: Uogolnic i przenisc cmp. JORDAN1A:15
  for A,B be Subset of TOP-REAL 2 st A meets B holds proj1.:A meets proj1.:B
proof
  let A,B be Subset of TOP-REAL 2;
  assume A meets B;
  then consider e be 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;
A3: e`1 = proj1.e by PSCOMP_1:def 5;
  then
A4: e`1 in proj1.:B by A2,FUNCT_2:35;
  e`1 in proj1.:A by A1,A3,FUNCT_2:35;
  hence thesis by A4,XBOOLE_0:3;
end;
