
theorem
  for A being non empty transitive AltCatStr for B being with_units non
  empty AltCatStr for F being feasible FunctorStr over A, B holds (id B) * F =
  the FunctorStr of F
proof
  let A be non empty transitive AltCatStr, B be with_units non empty
  AltCatStr, F be feasible FunctorStr over A, B;
A1: the ObjectMap of ((id B) * F) = (the ObjectMap of (id B))*the ObjectMap
  of F by FUNCTOR0:def 36
    .= (id [:the carrier of B, the carrier of B:])*the ObjectMap of F by
FUNCTOR0:def 29
    .= the ObjectMap of F by FUNCT_2:17;
A2: the MorphMap of F is ManySortedFunction of the Arrows of A, (the Arrows
  of B)*the ObjectMap of F by FUNCTOR0:def 4;
  the MorphMap of ((id B) * F) = ((the MorphMap of id B)*the ObjectMap of
  F)**the MorphMap of F by FUNCTOR0:def 36
    .= ((id the Arrows of B)*the ObjectMap of F)**the MorphMap of F by
FUNCTOR0:def 29
    .= the MorphMap of F by A2,Lm1;
  hence thesis by A1;
end;
