reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;
reserve s for State of 2GatesCircuit(x,y,c,f);

theorem
  for x,y,c being non pair object for s being State of MajorityCirc(x,y,c)
for a1,a2 being Element of BOOLEAN st a1 = s.x & a2 = s.y holds (Following s).[
  <*x,y*>,'&'] = a1 '&' a2
proof
  let x,y,c be non pair object;
  reconsider a = c as Vertex of MajorityStr(x,y,c) by Th72;
  let s be State of MajorityCirc(x,y,c);
  s.a is Element of BOOLEAN;
  hence thesis by Lm2;
end;
