let x, y, z be set ; :: thesis: InnerVertices (GFA2CarryIStr x,y,z) = {[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]}
set f1 = and2a ;
set f2 = and2c ;
set f3 = and2b ;
set xy = [<*x,y*>,and2a ];
set yz = [<*y,z*>,and2c ];
set zx = [<*z,x*>,and2b ];
set Cxy = 1GateCircStr <*x,y*>,and2a ;
set Cyz = 1GateCircStr <*y,z*>,and2c ;
set Czx = 1GateCircStr <*z,x*>,and2b ;
A1: 1GateCircStr <*x,y*>,and2a tolerates 1GateCircStr <*y,z*>,and2c by CIRCCOMB:55;
(1GateCircStr <*x,y*>,and2a ) +* (1GateCircStr <*y,z*>,and2c ) tolerates 1GateCircStr <*z,x*>,and2b by CIRCCOMB:55;
then InnerVertices (GFA2CarryIStr x,y,z) = (InnerVertices ((1GateCircStr <*x,y*>,and2a ) +* (1GateCircStr <*y,z*>,and2c ))) \/ (InnerVertices (1GateCircStr <*z,x*>,and2b )) by CIRCCOMB:15
.= ((InnerVertices (1GateCircStr <*x,y*>,and2a )) \/ (InnerVertices (1GateCircStr <*y,z*>,and2c ))) \/ (InnerVertices (1GateCircStr <*z,x*>,and2b )) by A1, CIRCCOMB:15
.= ({[<*x,y*>,and2a ]} \/ (InnerVertices (1GateCircStr <*y,z*>,and2c ))) \/ (InnerVertices (1GateCircStr <*z,x*>,and2b )) by CIRCCOMB:49
.= ({[<*x,y*>,and2a ]} \/ {[<*y,z*>,and2c ]}) \/ (InnerVertices (1GateCircStr <*z,x*>,and2b )) by CIRCCOMB:49
.= ({[<*x,y*>,and2a ]} \/ {[<*y,z*>,and2c ]}) \/ {[<*z,x*>,and2b ]} by CIRCCOMB:49
.= {[<*x,y*>,and2a ],[<*y,z*>,and2c ]} \/ {[<*z,x*>,and2b ]} by ENUMSET1:41
.= {[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]} by ENUMSET1:43 ;
hence InnerVertices (GFA2CarryIStr x,y,z) = {[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]} ; :: thesis: verum