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
  t is not root implies t is CompoundTerm of S,V
proof
  assume
A1: t is not root;
  per cases by Th2;
  suppose
    ex s being SortSymbol of S, v being Element of V.s st t.{} = [v,s];
    then consider s being SortSymbol of S, x being Element of V.s such that
A2: t.{} = [x,s];
    t = root-tree [x,s] by A2,Th5;
    hence thesis by A1;
  end;
  suppose
    t.{} in [:the carrier' of S,{the carrier of S}:];
    hence t.{} in [:the carrier' of S,{the carrier of S}:];
  end;
end;
