
theorem
  for A being with_units transitive non empty AltCatStr for B being
  with_units non empty AltCatStr for F being feasible FunctorStr over A, B
  holds F * (id A) = the FunctorStr of F
proof
  let A be with_units transitive non empty AltCatStr, B be with_units non
  empty AltCatStr, F be feasible FunctorStr over A, B;
A1: the ObjectMap of (F*(id A)) = (the ObjectMap of F)*the ObjectMap of id A
  by FUNCTOR0:def 36
    .= (the ObjectMap of F)*id [:the carrier of A, the carrier of A:] 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 (F*id A) = ((the MorphMap of F)*the ObjectMap of id A)**
  the MorphMap of id A by FUNCTOR0:def 36
    .= ((the MorphMap of F)*id [:the carrier of A, the carrier of A:]) **the
  MorphMap of id A by FUNCTOR0:def 29
    .= (the MorphMap of F)**the MorphMap of id A by FUNCTOR0:2
    .= (the MorphMap of F)**id the Arrows of A by FUNCTOR0:def 29
    .= the MorphMap of F by A2,MSUALG_3:3;
  hence thesis by A1;
end;
