
theorem Th2:
  for X being set holds union FlatCoh X = X
proof
  let X be set;
  hereby
    let x be object;
    assume x in union FlatCoh X;
    then consider y being set such that
A1: x in y and
A2: y in FlatCoh X by TARSKI:def 4;
    ex z being set st y = {z} & z in X by A1,A2,Th1;
    hence x in X by A1,TARSKI:def 1;
  end;
  let x be object;
  assume x in X;
  then x in {x} & {x} in FlatCoh X by Th1,TARSKI:def 1;
  hence thesis by TARSKI:def 4;
end;
