reserve  X for non empty set,
  R for Relation of X;
reserve O for non empty RelStr;

theorem Th11:
  O is QuasiOrdered implies O is SubQuasiOrdered
proof
  set IntRel = the InternalRel of O;
  set CO = the carrier of O;
  assume
A1: O is QuasiOrdered;
  then
A2: O is transitive;
  O is reflexive by A1;
  then IntRel is_reflexive_in CO;
  then IntRel is reflexive by PARTIT_2:21;
  hence thesis by A2,Def4;
end;
