reserve x,y for set;

theorem Th28:
  for A,B being category, C being non empty subcategory of A for F
being FunctorStr over A,B for a being Object of A, c being Object of C st c = a
  holds (F|C).c = F.a
proof
  let A,B be category, C be non empty subcategory of A;
  let F be FunctorStr over A,B;
  let b be Object of A;
  let a be Object of C;
  assume a = b;
  then (incl C).a = b by FUNCTOR0:27;
  hence thesis by FUNCTOR0:33;
end;
