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 Th25:
  for S being non empty ManySortedSign holds
  S, S are_equivalent_wrt id the carrier of S, id the carrier' of S
proof
  let S be non empty ManySortedSign;
  set f = id the carrier of S, g = id the carrier' of S;
  thus f is one-to-one;
A1: f" = f by FUNCT_1:45;
  g" = g by FUNCT_1:45;
  hence thesis by A1,INSTALG1:8;
end;
