
theorem
  for S1 being non empty ManySortedSign for S2 being non empty
Subsignature of S1 for A being MSAlgebra over S1 holds (id the Sorts of A)|the
  carrier of S2 = id the Sorts of A|S2
proof
  let S1 be non empty ManySortedSign;
  let S2 be non empty Subsignature of S1;
  set f = id the carrier of S2, g = id the carrier' of S2;
  let A be MSAlgebra over S1;
  f,g form_morphism_between S2,S1 by Def2;
  then (id the Sorts of A)*f = id the Sorts of A|S2 by Th31;
  hence thesis by RELAT_1:65;
end;
