theorem Th32:
  G1 is_naturally_transformable_to G2 implies t*id B = t
proof
  assume
A1: G1 is_naturally_transformable_to G2;
A2: G1*id B = G1 by FUNCT_2:17;
  then reconsider s = t*id B as natural_transformation of G1,G2 by FUNCT_2:17;
A3: G2*id B = G2 by FUNCT_2:17;
  now
    let b be Object of B;
    thus s.b = t.((id B).b) by A1,A2,A3,Th22
      .= t.b by CAT_1:79;
  end;
  hence thesis by A1,Th24;
end;
