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

theorem Th50:
  for a being Object of c1Cat*(o,m) holds a is initial
proof
  let a be Object of c1Cat*(o,m);
  let b be Object of c1Cat*(o,m);
  set f = the Morphism of a,b;
  thus Hom(a,b)<>{} by Th47;
  take f;
  thus thesis by Th46;
end;
