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,a3 being Element of BOOLEAN st a1 = s.x & a2 = s.y & a3 = s.c holds (
Following(s,2)).MajorityOutput(x,y,c) = a1 '&' a2 'or' a2 '&' a3 'or' a3 '&' a1
  by Lm3;
