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 D1,D2 being full non empty SubCatStr of C st the carrier of D1 =
  the carrier of D2 holds the AltCatStr of D1 = the AltCatStr of D2
proof
  let D1,D2 be full non empty SubCatStr of C;
  assume
A1: the carrier of D1 = the carrier of D2;
  then the Arrows of D1 =(the Arrows of C)||the carrier of D2 by Def13
    .= the Arrows of D2 by Def13;
  hence thesis by A1,Th26;
end;
