
theorem
  for C being associative transitive non empty AltCatStr, o1,o2,o3
being Object of C st <^o1,o2^> <> {} & <^o2,o3^> <> {} for A being Morphism of
  o1,o2, B being Morphism of o2,o3 st B * A is mono holds A is mono
proof
  let C be associative transitive non empty AltCatStr, o1,o2,o3 be Object of
  C;
  assume
A1: <^o1,o2^> <> {} & <^o2,o3^> <> {};
  let A be Morphism of o1,o2, B be Morphism of o2,o3;
  assume
A2: B * A is mono;
  let o be Object of C;
  assume
A3: <^o,o1^> <> {};
  let M1,M2 be Morphism of o,o1;
  assume
A4: A*M1 = A*M2;
  (B*A)*M1 = B*(A*M1) & (B*A)*M2 = B*(A*M2) by A1,A3,ALTCAT_1:21;
  hence thesis by A2,A3,A4;
end;
