reserve C for category,
  o1, o2, o3 for Object of C;

theorem Th35:
  for C being with_units non empty AltCatStr, D being SubCatStr
of C st the carrier of C = the carrier of D & the Arrows of C = the Arrows of D
  holds D is id-inheriting
proof
  let C be with_units non empty AltCatStr, D be SubCatStr of C;
  assume
  the carrier of C = the carrier of D & the Arrows of C = the Arrows of D;
  then reconsider D as full non empty SubCatStr of C by Th34;
  now
    let o be Object of D, o9 be Object of C;
    assume o = o9;
    then <^o9,o9^> = <^o,o^> by ALTCAT_2:28;
    hence idm o9 in <^o,o^>;
  end;
  hence thesis by ALTCAT_2:def 14;
end;
