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
  for t being c-Term of A,V for s being SortSymbol of S, x being set st
  x in (the Sorts of A).s & t.{} = [x,s] holds t = root-tree [x,s]
proof
  let t be c-Term of A,V;
  let s be SortSymbol of S, x be set;
  set G = DTConMSA ((the Sorts of A) (\/) V);
  reconsider t as Element of TS G;
  assume x in (the Sorts of A).s;
  then reconsider a = [x,s] as Terminal of G by Lm4;
  t.{} = a implies t = root-tree a by DTCONSTR:9;
  hence thesis;
end;
