reserve U1,U2,U3 for Universal_Algebra,
  m,n for Nat,
  a for set,
  A for non empty set,
  h for Function of U1,U2;

theorem Th10:
  for U1,U2 st U1,U2 are_similar holds MSSign U1 = MSSign U2
proof
  let U1,U2 such that
A1: U1,U2 are_similar;
  reconsider f = (*-->0)*(signature U1) as Function of dom signature(U1), {0}*
  by MSUALG_1:2;
A2: the carrier of MSSign U1 = {0} & the Arity of MSSign U1 = f by
MSUALG_1:def 8;
  reconsider f = (*-->0)*(signature U2) as Function of dom signature(U2), {0}*
  by MSUALG_1:2;
A3: the Arity of MSSign U2 = f & the ResultSort of MSSign U2 = dom signature
  U2 -->0 by MSUALG_1:def 8;
A4: the ResultSort of MSSign U1 = dom signature U1-->0 & the carrier of
  MSSign U2 = {0} by MSUALG_1:def 8;
 the carrier' of MSSign U1 = dom signature U1 & the carrier' of MSSign U2
  = dom signature U2 by MSUALG_1:def 8;
  then the carrier' of MSSign U1 = the carrier' of MSSign U2 by A1;
  hence thesis by A1,A2,A4,A3;
end;
