reserve X,Y for set;
reserve Z for non empty set;

theorem
  for A,I being non empty reflexive AltCatStr, B being non empty
  reflexive SubCatStr of A, C being non empty SubCatStr of A, D being non empty
  SubCatStr of B st C = D for F being FunctorStr over A,I holds F|C = F|B|D
proof
  let A,I be non empty reflexive AltCatStr, B be non empty reflexive SubCatStr
  of A, C be non empty SubCatStr of A, D be non empty SubCatStr of B such that
A1: C = D;
  let F be FunctorStr over A,I;
  thus F|C = F * (incl B * incl D) by A1,Th4
    .= F|B|D by FUNCTOR0:32;
end;
