
theorem Th25:
  for S being non empty ManySortedSign for A being MSAlgebra over
  S holds A|(S, id the carrier of S, id the carrier' of S) = the MSAlgebra of A
proof
  let S be non empty ManySortedSign;
  let A be MSAlgebra over S;
  set f = id the carrier of S, g = id the carrier' of S;
  dom the Charact of A = the carrier' of S by PARTFUN1:def 2;
  then
A1: the Charact of the MSAlgebra of A = (the Charact of A)*g by RELAT_1:52;
  dom the Sorts of A = the carrier of S by PARTFUN1:def 2;
  then
A2: the Sorts of the MSAlgebra of A = (the Sorts of A)*f by RELAT_1:52;
  f,g form_morphism_between S,S by Th8;
  hence thesis by A2,A1,Def3;
end;
