theorem
  f is epi & g is epi implies g*f is epi
proof
  assume that
A1: f is epi and
A2: g is epi;
A3: Hom(a,b)<>{} by A1;
A4: Hom(b,c)<>{} by A2;
A5: now
    let d,h1,h2 such that
A6: Hom(c,d)<>{} and
A7: h1*(g*f) = h2*(g*f);
A8: Hom(b,d) <> {} by A4,A6,Th19;
    h1*(g*f) = (h1*g)*f & (h2*g)*f = h2*(g*f) by A3,A4,A6,Th21;
    then h1*g = h2*g by A1,A7,A8;
    hence h1 = h2 by A2,A6;
  end;
  Hom(a,c) <> {} by A3,A4,Th19;
  hence thesis by A5;
end;
