reserve IIG for Circuit-like non void non empty ManySortedSign;
reserve IIG for monotonic Circuit-like non void non empty ManySortedSign;

theorem
  for IIG for A being finite-yielding non-empty MSAlgebra over IIG, v
  being Vertex of IIG, e being Element of (the Sorts of FreeEnv A).v st v in (
  InnerVertices IIG \ SortsWithConstants IIG) & card e = size(v,A) ex o being
  OperSymbol of IIG st e.{} = [o,the carrier of IIG]
proof
  let IIG;
  let A be finite-yielding non-empty MSAlgebra over IIG, v be Vertex of IIG, e
  be Element of (the Sorts of FreeEnv A).v;
  assume
  v in (InnerVertices IIG \ SortsWithConstants IIG) & card e = size(v, A);
  then
A1: ex q being DTree-yielding FinSequence st e = [action_at v,the carrier of
  IIG]-tree q by Th12;
  take action_at v;
  thus thesis by A1,TREES_4:def 4;
end;
