reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem
  for f being Morphism of a,b st Hom(a,b) <> {} holds <:f,f:> = Delta(b) *f
proof
  let f be Morphism of a,b such that
A1: Hom(a,b) <> {};
  Hom(b,b) <> {} & (id b)*f = f by A1,CAT_1:28;
  hence thesis by A1,Th25;
end;
