
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 coretraction holds A is coretraction
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 coretraction;
  then consider G be Morphism of o3,o1 such that
A2: G is_left_inverse_of (B * A);
A3: (G * B) * A = G * (B * A) by A1,ALTCAT_1:21;
  G * (B * A) = idm o1 by A2;
  then G * B is_left_inverse_of A by A3;
  hence thesis;
end;
