
theorem
  for C being category, o1,o2,o3 being Object of C, A being Morphism of
o1, o2, B being Morphism of o2,o3 st <^o1,o2^> <> {} & <^o2,o3^> <> {} & <^o3,
  o1^> <> {} & B * A is retraction holds B is retraction
proof
  let C be category, o1,o2,o3 be Object of C, A be Morphism of o1,o2, B be
  Morphism of o2,o3;
  assume
A1: <^o1,o2^> <> {} & <^o2,o3^> <> {} & <^o3,o1^> <> {};
  assume B * A is retraction;
  then consider G be Morphism of o3,o1 such that
A2: G is_right_inverse_of (B*A);
  (B * A) * G = idm o3 by A2;
  then B * (A * G) = idm o3 by A1,ALTCAT_1:21;
  then A * G is_right_inverse_of B;
  hence thesis;
end;
