reserve x, y for set;

theorem Th3:
  for C being lattice-wise 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*@f
proof
  let C be lattice-wise category;
  let a,b,c be Object of C such that
A1: <^a,b^> <> {} & <^b,c^> <> {};
  let f be Morphism of a,b, g be Morphism of b,c;
  f = @f & g = @g by A1,Def7;
  hence thesis by A1,YELLOW18:36;
end;
