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,a3 being Element of BOOLEAN st a1 = s.x & a3 = s.c holds (Following(s,2)
  ).[<*c,x*>,'&'] = a3 '&' a1
proof
  let x,y,c be non pair object;
  reconsider a = y 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 Lm3;
end;
