reserve X for BCI-algebra;
reserve X1 for non empty Subset of X;
reserve A,I for Ideal of X;
reserve x,y,z for Element of X;
reserve a for Element of A;

theorem
  initial_section(a) c= A
proof
  let b be object;
  assume b in initial_section(a);
  then ex x1 being Element of X st b=x1 & x1<=a;
  hence thesis by Th5;
end;
