
theorem Th36:
  for C being para-functional semi-functional category
  for a,b,c being Object of C st <^a,b^> <> {} & <^b,c^> <> {}
  for f being Morphism of a,b, g being Morphism of b,c
  holds g*f = (g qua Function)*(f qua Function)
proof
  let C be para-functional semi-functional category;
  let a,b,c be Object of C such that
A1: <^a,b^> <> {} and
A2: <^b,c^> <> {};
  let f be Morphism of a,b, g be Morphism of b,c;
  <^a,c^> <> {} by A1,A2,ALTCAT_1:def 2;
  hence thesis by A1,A2,ALTCAT_1:def 12;
end;
