theorem
  Hom(a,b) <> {} & a is terminal implies f is monic
proof
  assume that
A1: Hom(a,b) <> {} and
A2: a is terminal;
  now
    let c be (Object of C),g,h be Morphism of c,a such that
    Hom(c,a)<>{} and
    f*g=f*h;
    consider ff being Morphism of c,a such that
A3: for gg being Morphism of c,a holds ff=gg by A2;
    ff = g by A3;
    hence g=h by A3;
  end;
  hence thesis by A1;
end;
