reserve a, I for set,
  S for non empty non void ManySortedSign;
reserve A, M for ManySortedSet of I,
  B, C for non-empty ManySortedSet of I;

theorem
  for A being MSAlgebra over S st ex X being ManySortedSet of the
carrier of S st the Sorts of A = {X} holds A, Trivial_Algebra S are_isomorphic
proof
  let A be MSAlgebra over S such that
A1: ex X being ManySortedSet of the carrier of S st the Sorts of A = {X};
  set I = the carrier of S, SB = the Sorts of A, ST = the Sorts of
  Trivial_Algebra S;
  consider X being ManySortedSet of I such that
A2: the Sorts of A = {X} by A1;
  set F = the ManySortedFunction of SB, ST;
  reconsider F1 = F as ManySortedFunction of {X}, ST by A2;
  take F;
  A is non-empty by A2;
  hence F is_epimorphism A, Trivial_Algebra S by Th25;
  hence F is_homomorphism A, Trivial_Algebra S;
  F1 is "1-1" by Th10;
  hence thesis;
end;
