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

theorem Th51:
  for c being Object of c1Cat*(o,m), i1,i2 being Morphism of
  c1Cat*(o,m) holds c is_a_coproduct_wrt i1,i2
proof
  let c be Object of c1Cat*(o,m), i1,i2 be Morphism of c1Cat*(o,m);
  thus cod i1 = c & cod i2 = c by Th45;
  let d be Object of c1Cat*(o,m), f,g be Morphism of c1Cat*(o,m) such that
  f in Hom(dom i1,d) and
  g in Hom(dom i2,d);
  take h = i1;
  thus h in Hom(c,d) by Th47;
  thus thesis by Th46;
end;
