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 Th65:
  Hom(a,c) <> {} & Hom(b,c) <> {} implies Hom(a+b,c) <> {}
proof
A1: a+b is_a_coproduct_wrt in1(a,b),in2(a,b) by Def26;
  Hom(a,a+b) <> {} & Hom(b,a+b) <> {} by Th61;
  hence thesis by A1,CAT_3:81;
end;
