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;
reserve S for non void non empty ManySortedSign,
  A for non-empty MSAlgebra over S,
  V for Variables of A,
  t for c-Term of A,V,
  f for ManySortedFunction of V, the Sorts of A;
reserve t for c-Term of A,V;

theorem
  for s being SortSymbol of S, x being Element of (the Sorts of A).s
  holds (x-term(A,V))@f = x
proof
  let s be SortSymbol of S, x be Element of (the Sorts of A).s;
  x = (root-tree x).{} by TREES_4:3;
  hence thesis by Th31,Th39;
end;
