reserve e for set;
reserve C,C1,C2,C3 for AltCatStr;
reserve C for non empty AltCatStr,
  o for Object of C;
reserve C for non empty transitive AltCatStr;

theorem Th29:
  for C being non empty AltCatStr, D being non empty SubCatStr of
  C for o being Object of D holds o is Object of C
proof
  let C be non empty AltCatStr, D be non empty SubCatStr of C;
  let o be Object of D;
  o in the carrier of D & the carrier of D c= the carrier of C by Def11;
  hence thesis;
end;
