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 Th5: ::proposition 1.4.1
  x<=a implies x in A
proof
  assume x<=a;
  then x\a = 0.X;
  then x\a in A by BCIALG_1:def 18;
  hence thesis by BCIALG_1:def 18;
end;
