reserve S for non void non empty ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S;
reserve A for MSAlgebra over S,
  t for Term of S,V;

theorem Th30:
  for V being Variables of A for s being SortSymbol of S, x being
  set st x in (the Sorts of A).s for v being Element of V.s holds x <> v
proof
  let V be Variables of A;
  let s be SortSymbol of S, x be set such that
A1: x in (the Sorts of A).s;
  let v be Element of V.s;
  V misses the Sorts of A by Def8;
  then V.s misses (the Sorts of A).s;
  hence thesis by A1,XBOOLE_0:3;
end;
