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 Th72:
  x in the carrier of MajorityStr(x,y,c) & y in the carrier of
  MajorityStr(x,y,c) & c in the carrier of MajorityStr(x,y,c)
proof
  c in the carrier of 1GateCircStr(<*c,x*>, '&') by Th43;
  then
A1: c in the carrier of MajorityIStr(x,y,c) by Th20;
  y in the carrier of 1GateCircStr(<*x,y*>, '&') by Th43;
  then y in the carrier of 1GateCircStr(<*x,y*>, '&')+*1GateCircStr(<*y,c*> ,
  '&') by Th20;
  then
A2: y in the carrier of MajorityIStr(x,y,c) by Th20;
  x in the carrier of 1GateCircStr(<*c,x*>, '&') by Th43;
  then x in the carrier of MajorityIStr(x,y,c) by Th20;
  hence thesis by A2,A1,Th20;
end;
