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 Th34:
  for S being non empty ManySortedSign for C being non-empty MSAlgebra over S
  holds id the carrier of S, id the carrier' of S form_embedding_of C, C
proof
  let S be non empty ManySortedSign;
  let C be non-empty MSAlgebra over S;
  thus id the carrier of S is one-to-one;
A1: dom the Sorts of C = the carrier of S by PARTFUN1:def 2;
  dom the Charact of C = the carrier' of S by PARTFUN1:def 2;
  hence thesis by A1,INSTALG1:8,RELAT_1:52;
end;
