theorem Th26:
  G1 is_naturally_transformable_to G2 & G2
  is_naturally_transformable_to G3 implies (t9`*`t)*F = (t9*F)`*`(t*F)
proof
  assume
A1: G1 is_naturally_transformable_to G2 & G2 is_naturally_transformable_to G3;
  then
A2: G1*F is_naturally_transformable_to G2*F & G2*F
  is_naturally_transformable_to G3*F by Th20;
  now
    let a be Object of A;
A3: G1.(F.a) = (G1*F).a & G2.(F.a) = (G2*F).a by CAT_1:76;
A4: G3.(F.a) = (G3*F).a by CAT_1:76;
A5: t9.(F.a) = (t9*F).a & t.(F.a) = (t*F).a by A1,Th22;
    thus ((t9`*`t)*F).a = (t9`*`t).(F.a) by A1,Th22,NATTRA_1:23
      .= (t9.(F.a))*(t.(F.a)) by A1,NATTRA_1:25
      .= ((t9*F)`*`(t*F)).a by A2,A5,A3,A4,NATTRA_1:25;
  end;
  hence thesis by A2,Th24,NATTRA_1:23;
end;
