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 Th67:
  InnerVertices MajorityStr(x,y,c) is Relation
proof
A1: InnerVertices 1GateCircStr(<*[<*x,y*>, '&'], [<*y,c*>, '&'], [<*c,x*>,
  '&']*>, or3) is Relation by Th38;
  InnerVertices 1GateCircStr(<*x,y*>,'&') is Relation & InnerVertices
  1GateCircStr(<*y,c*>,'&') is Relation by Th38;
  then
A2: InnerVertices (1GateCircStr(<*x,y*>,'&')+*1GateCircStr(<*y,c*>,'&')) is
  Relation by Th2,CIRCCOMB:47;
  InnerVertices 1GateCircStr(<*c,x*>,'&') is Relation by Th38;
  then InnerVertices MajorityIStr(x,y,c) is Relation by A2,Th2,CIRCCOMB:47;
  hence thesis by A1,Th2,CIRCCOMB:47;
end;
