reserve U0,U1,U2,U3 for Universal_Algebra,
  n for Nat,
  x,y for set;

theorem
  U1,U2 are_similar implies len the charact of(U1) = len the charact of( U2)
proof
A1: len signature (U1) = len the charact of(U1) & len signature (U2) = len
  the charact of(U2) by UNIALG_1:def 4;
  assume U1,U2 are_similar;
  hence thesis by A1;
end;
