reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;

theorem Th56:
  InnerVertices 2GatesCircStr(x,y,c,f) = {[<*x,y*>, f],
  2GatesCircOutput(x,y,c,f)}
proof
  set p = <*[<*x,y*>, f], c*>;
  set S1 = 1GateCircStr(<*x,y*>, f), S2 = 1GateCircStr(p, f);
  set S = 2GatesCircStr(x,y,c,f);
  S1 tolerates S2 by CIRCCOMB:43;
  hence InnerVertices S = (InnerVertices S1) \/ (InnerVertices S2) by
CIRCCOMB:11
    .= {[<*x,y*>, f]} \/ (InnerVertices S2) by CIRCCOMB:42
    .= {[<*x,y*>, f]} \/ {[p, f]} by CIRCCOMB:42
    .= {[<*x,y*>, f], 2GatesCircOutput(x,y,c,f)} by ENUMSET1:1;
end;
