theorem
  Hom(a,b)<>{} & Hom(b,c)<>{} & g*f is epi implies g is epi
proof
  assume that
A1: Hom(a,b)<>{} and
A2: Hom(b,c)<>{} and
A3: g*f is epi;
  now
    let d,h1,h2;
    assume
A4: Hom(c,d)<>{};
    then h1*(g*f) = (h1*g)*f & h2*(g*f) = (h2*g)*f by A1,A2,Th21;
    hence h1*g = h2*g implies h1 = h2 by A3,A4;
  end;
  hence thesis by A2;
end;
