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 Th20:
  for o being OperSymbol of S, p being ArgumentSeq of Sym(o,V)
  holds the_sort_of (Sym(o,V)-tree p qua Term of S,V) = the_result_sort_of o
proof
  let o be OperSymbol of S, p be ArgumentSeq of Sym(o,V);
A1: ([o,the carrier of S]-tree p).{} = [o,the carrier of S] by TREES_4:def 4;
  [o,the carrier of S] = Sym(o,V) by MSAFREE:def 9;
  hence thesis by A1,Th17;
end;
