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 Th73:
  [<*x,y*>,'&'] in InnerVertices MajorityStr(x,y,c) & [<*y,c*>,'&'
  ] in InnerVertices MajorityStr(x,y,c) & [<*c,x*>,'&'] in InnerVertices
  MajorityStr(x,y,c)
proof
  [<*x,y*>,'&'] in InnerVertices 1GateCircStr(<*x,y*>, '&') by Th47;
  then
  [<*x,y*>,'&'] in InnerVertices (1GateCircStr(<*x,y*>, '&')+*1GateCircStr
  (<*y,c*>, '&')) by Th21;
  then
A1: [<*x,y*>,'&'] in InnerVertices MajorityIStr(x,y,c) by Th21;
  [<*y,c*>,'&'] in InnerVertices 1GateCircStr(<*y,c*>, '&') by Th47;
  then
  [<*y,c*>,'&'] in InnerVertices (1GateCircStr(<*x,y*>, '&')+*1GateCircStr
  (<*y,c*>, '&')) by Th21;
  then
A2: [<*y,c*>,'&'] in InnerVertices MajorityIStr(x,y,c) by Th21;
  [<*c,x*>,'&'] in InnerVertices 1GateCircStr(<*c,x*>, '&') by Th47;
  then [<*c,x*>,'&'] in InnerVertices MajorityIStr(x,y,c) by Th21;
  hence thesis by A1,A2,Th21;
end;
