reserve S for non void non empty ManySortedSign,
  U1,U2 for MSAlgebra over S,
  o for OperSymbol of S,
  n for Nat;

theorem
  for U1,U2 being non-empty MSAlgebra over S holds U1,U2 are_isomorphic
  implies U2,U1 are_isomorphic
proof
  let U1,U2 be non-empty MSAlgebra over S;
  assume U1,U2 are_isomorphic;
  then consider F be ManySortedFunction of U1,U2 such that
A1: F is_isomorphism U1,U2;
  reconsider G = F"" as ManySortedFunction of U2,U1;
  G is_isomorphism U2,U1 by A1,Th14;
  hence thesis;
end;
