
theorem Th2:
  for C being category, o1,o2 being Object of C st <^o1,o2^> <> {}
  & <^o2,o1^> <> {} for A being Morphism of o1,o2 st A is retraction & A is
  coretraction holds A" * A = idm o1 & A * A" = idm o2
proof
  let C be category, o1,o2 be Object of C such that
A1: <^o1,o2^> <> {} & <^o2,o1^> <> {};
  let A be Morphism of o1,o2;
  assume A is retraction & A is coretraction;
  then A" is_left_inverse_of A & A" is_right_inverse_of A by A1,Def4;
  hence thesis;
end;
