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
  for D being full SubCatStr of C st the carrier of D = the carrier of C
  holds the AltCatStr of D = the AltCatStr of C
proof
  let D be full SubCatStr of C such that
A1: the carrier of D = the carrier of C;
  the Arrows of D = (the Arrows of C)||the carrier of D by Def13
    .= the Arrows of C by A1;
  hence thesis by A1,Th25;
end;
