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 Th5:
  for s being SortSymbol of S, v being Element of V.s st t.{} = [v,
  s] holds t = root-tree [v,s]
proof
  let s be SortSymbol of S, x be Element of V.s;
  set G = DTConMSA V;
  reconsider a = [x,s] as Terminal of G by Lm3;
  reconsider t as Element of TS G;
  t.{} = a implies t = root-tree a by DTCONSTR:9;
  hence thesis;
end;
