reserve A for non empty AltCatStr,
  B, C for non empty reflexive AltCatStr,
  F for feasible Covariant FunctorStr over A, B,
  G for feasible Covariant FunctorStr over B, C,
  M for feasible Contravariant FunctorStr over A, B,
  N for feasible Contravariant FunctorStr over B, C,
  o1, o2 for Object of A,
  m for Morphism of o1, o2;
reserve A, B, C, D for transitive with_units non empty AltCatStr,
  F1, F2, F3 for covariant Functor of A, B,
  G1, G2, G3 for covariant Functor of B, C,
  H1, H2 for covariant Functor of C, D,
  p for transformation of F1, F2,
  p1 for transformation of F2, F3,
  q for transformation of G1, G2,
  q1 for transformation of G2, G3,
  r for transformation of H1, H2;

theorem
  G1 is_transformable_to G2 implies q(#)(idt id B) = q
proof
  assume
A1: G1 is_transformable_to G2;
  then
A2: G1*(id B) is_transformable_to G2*(id B) by Th10;
  thus q(#)(idt id B) = (q*(id B))`*`(idt (G1*id B)) by Th19
    .= q*id B by A2,FUNCTOR2:5
    .= q by A1,Th21;
end;
