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 Th61:
  Hom(a,a+b) <> {} & Hom(b,a+b) <> {}
proof
  set c = (the Coproduct of C).(a,b);
  set i1 = (the Incl1 of C).(a,b), i2 = (the Incl2 of C).(a,b);
  c is_a_coproduct_wrt i1,i2 by Def26;
  then
A1: cod i1 = c & cod i2 = c;
  dom(i1) = a & dom(i2) = b by Def26;
  hence thesis by A1,CAT_1:1;
end;
