
theorem
  for X be non empty set for Y be finite Subset-Family of X st Y is
  in_general_position holds Components(Y) is a_partition of X
proof
  let X be non empty set;
  let Y be finite Subset-Family of X;
  assume Y is in_general_position;
  then
A1: for A be Subset of X st A in Components(Y) holds A <> {} & for B be
  Subset of X st B in Components(Y) holds A = B or A misses B by Th16;
  union Components(Y) = X by Th15;
  hence thesis by A1,EQREL_1:def 4;
end;
