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
  Hom(a,b) <> {} & Hom(b,a) <> {} implies in1(a,b) is coretraction & in2
  (a,b) is coretraction
proof
A1:  Hom(a,a+b) <> {} & Hom(b,a+b) <> {} by Th61;
  a+b is_a_coproduct_wrt in1(a,b),in2(a,b) & dom in1(a,b) = a by Def26;
  hence thesis by A1,CAT_3:82;
end;
