
theorem
  for S being with_nonpair_inputs non empty ManySortedSign for x being
  Vertex of S st x is pair holds x in InnerVertices S
proof
  let S be with_nonpair_inputs non empty ManySortedSign;
  let x be Vertex of S;
  the carrier of S = (InputVertices S) \/ InnerVertices S by XBOOLE_1:45;
  then x in InputVertices S or x in InnerVertices S by XBOOLE_0:def 3;
  hence thesis by FACIRC_1:def 2;
end;
