let x, y, c be set ; :: thesis: InnerVertices (MajorityIStr x,y,c) = {[<*x,y*>,'&' ],[<*y,c*>,'&' ],[<*c,x*>,'&' ]}
A1:
(1GateCircStr <*x,y*>,'&' ) +* (1GateCircStr <*y,c*>,'&' ) tolerates 1GateCircStr <*c,x*>,'&'
by CIRCCOMB:55;
A2:
1GateCircStr <*x,y*>,'&' tolerates 1GateCircStr <*y,c*>,'&'
by CIRCCOMB:55;
InnerVertices (MajorityIStr x,y,c) =
(InnerVertices ((1GateCircStr <*x,y*>,'&' ) +* (1GateCircStr <*y,c*>,'&' ))) \/ (InnerVertices (1GateCircStr <*c,x*>,'&' ))
by A1, CIRCCOMB:15
.=
((InnerVertices (1GateCircStr <*x,y*>,'&' )) \/ (InnerVertices (1GateCircStr <*y,c*>,'&' ))) \/ (InnerVertices (1GateCircStr <*c,x*>,'&' ))
by A2, CIRCCOMB:15
.=
({[<*x,y*>,'&' ]} \/ (InnerVertices (1GateCircStr <*y,c*>,'&' ))) \/ (InnerVertices (1GateCircStr <*c,x*>,'&' ))
by CIRCCOMB:49
.=
({[<*x,y*>,'&' ]} \/ {[<*y,c*>,'&' ]}) \/ (InnerVertices (1GateCircStr <*c,x*>,'&' ))
by CIRCCOMB:49
.=
({[<*x,y*>,'&' ]} \/ {[<*y,c*>,'&' ]}) \/ {[<*c,x*>,'&' ]}
by CIRCCOMB:49
.=
{[<*x,y*>,'&' ],[<*y,c*>,'&' ]} \/ {[<*c,x*>,'&' ]}
by ENUMSET1:41
.=
{[<*x,y*>,'&' ],[<*y,c*>,'&' ],[<*c,x*>,'&' ]}
by ENUMSET1:43
;
hence
InnerVertices (MajorityIStr x,y,c) = {[<*x,y*>,'&' ],[<*y,c*>,'&' ],[<*c,x*>,'&' ]}
; :: thesis: verum