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 Th39:
  for vt being finite DecoratedTree st vt is_an_evaluation_of t,f
  holds t@f = vt.{}
proof
A1: ex e being finite DecoratedTree st e is_an_evaluation_of t,f & t@f = e
  .{} by Def10;
  let vt be finite DecoratedTree;
  assume vt is_an_evaluation_of t,f;
  hence thesis by A1,Th37;
end;
