theorem
  for S being non empty ManySortedSign for C being non-empty MSAlgebra over S
  holds C, C are_similar_wrt id the carrier of S, id the carrier' of S
proof
  let S be non empty ManySortedSign;
  let C be non-empty MSAlgebra over S;
  set f = id the carrier of S, g = id the carrier' of S;
A1: f" = f by FUNCT_1:45;
  g" = g by FUNCT_1:45;
  hence f, g form_embedding_of C, C & f", g" form_embedding_of C, C by A1,Th34;
end;
