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

theorem
  C is with_finite_coproduct
proof
A1: for a,b ex c being Object of C, i1,i2 being Morphism of C st dom i1 = a
  & dom i2 = b & cod i1 = c & cod i2 = c & c is_a_coproduct_wrt i1,i2
  proof
    let a,b;
    take a+b, in1(a,b), in2(a,b);
    thus thesis by Def26,Th59,Th60;
  end;
  EmptyMS C is initial by Def26;
  hence thesis by A1,Th44;
end;
