reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem Th26:
  not a in InitSegm(S,a)
proof
  assume not thesis;
  then a in LowerCone{a} by XBOOLE_0:def 4;
  then
A1: ex a1 st a = a1 & for a2 st a2 in {a} holds a1 < a2;
  a in {a} by TARSKI:def 1;
  hence thesis by A1;
end;
