
theorem Th10:
  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 A is epi & B is epi holds B * A is epi
proof
  let C be associative transitive non empty AltCatStr, o1,o2,o3 be Object of
  C;
  assume that
A1: <^o1,o2^> <> {} and
A2: <^o2,o3^> <> {};
  let A be Morphism of o1,o2, B be Morphism of o2,o3;
  assume that
A3: A is epi and
A4: B is epi;
  let o be Object of C;
  assume
A5: <^o3,o^> <> {};
  then
A6: <^o2,o^> <> {} by A2,ALTCAT_1:def 2;
  let M1,M2 be Morphism of o3,o;
  assume
A7: M1*(B*A) = M2*(B*A);
  M1*(B*A) = (M1*B)*A & M2*(B*A) = (M2*B)*A by A1,A2,A5,ALTCAT_1:21;
  then M1*B = M2*B by A3,A7,A6;
  hence thesis by A4,A5;
end;
