
theorem Th4:
  for C being category, o being Object of C holds (idm o)" = idm o
proof
  let C be category, o be Object of C;
A1: <^o,o^> <> {} by ALTCAT_1:19;
  idm o is retraction & idm o is coretraction by Th1;
  then
A2: (idm o)" is_left_inverse_of (idm o) by A1,Def4;
  thus (idm o)" = (idm o)" * idm o by A1,ALTCAT_1:def 17
    .= idm o by A2;
end;
