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;
