reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;
reserve S for non empty non void ManySortedSign,
  A for non-empty finite-yielding MSAlgebra over S,
  V for Variables of A,
  X for SetWithCompoundTerm of S,V;

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;
