
theorem Th17:
  for x,y,c being set holds InnerVertices MajorityIStr(x,y,c) =
  {[<*x,y*>,'&'], [<*y,c*>,'&'], [<*c,x*>,'&']}
proof
  let x,y,c be set;
A1: 1GateCircStr(<*x,y*>,'&') +* 1GateCircStr(<*y,c*>,'&') tolerates
  1GateCircStr(<*c,x*>,'&') by CIRCCOMB:47;
A2: 1GateCircStr(<*x,y*>,'&') tolerates 1GateCircStr(<*y,c*>,'&')
  by CIRCCOMB:47;
  InnerVertices MajorityIStr(x,y,c) =
  InnerVertices(1GateCircStr(<*x,y*>,'&') +* 1GateCircStr(<*y,c*>,'&')) \/
  InnerVertices(1GateCircStr(<*c,x*>,'&')) by A1,CIRCCOMB:11
    .= InnerVertices(1GateCircStr(<*x,y*>,'&')) \/
  InnerVertices(1GateCircStr(<*y,c*>,'&')) \/
  InnerVertices(1GateCircStr(<*c,x*>,'&')) by A2,CIRCCOMB:11
    .= {[<*x,y*>,'&']} \/ InnerVertices(1GateCircStr(<*y,c*>,'&')) \/
  InnerVertices(1GateCircStr(<*c,x*>,'&')) by CIRCCOMB:42
    .= {[<*x,y*>,'&']} \/ {[<*y,c*>,'&']} \/
  InnerVertices(1GateCircStr(<*c,x*>,'&')) by CIRCCOMB:42
    .= {[<*x,y*>,'&']} \/ {[<*y,c*>,'&']} \/ {[<*c,x*>,'&']} by CIRCCOMB:42
    .= {[<*x,y*>,'&'],[<*y,c*>,'&']} \/ {[<*c,x*>,'&']} by ENUMSET1:1
    .= {[<*x,y*>,'&'],[<*y,c*>,'&'],[<*c,x*>,'&']} by ENUMSET1:3;
  hence thesis;
end;
