reserve C for category,
  o1, o2, o3 for Object of C;

theorem
  for C being non empty AltCatStr, O, A being Object of C for M being
  Morphism of O, A st O is terminal holds M is mono
proof
  let C be non empty AltCatStr, O, A be Object of C, M be Morphism of O, A
  such that
A1: O is terminal;
  let o be Object of C such that
A2: <^o,O^> <> {};
  let a, b be Morphism of o, O such that
  M * a = M * b;
  consider N being Morphism of o, O such that
  N in <^o,O^> and
A3: for M1 being Morphism of o, O st M1 in <^o,O^> holds N = M1 by A1,
ALTCAT_3:27;
  thus a = N by A2,A3
    .= b by A2,A3;
end;
