let x, y, z be set ; :: thesis: InnerVertices (GFA3CarryIStr (x,y,z)) = {[<*x,y*>,nor2],[<*y,z*>,nor2],[<*z,x*>,nor2]}
set f1 = nor2 ;
set f2 = nor2 ;
set f3 = nor2 ;
set xy = [<*x,y*>,nor2];
set yz = [<*y,z*>,nor2];
set zx = [<*z,x*>,nor2];
set Cxy = 1GateCircStr (<*x,y*>,nor2);
set Cyz = 1GateCircStr (<*y,z*>,nor2);
set Czx = 1GateCircStr (<*z,x*>,nor2);
A1: 1GateCircStr (<*x,y*>,nor2) tolerates 1GateCircStr (<*y,z*>,nor2) by CIRCCOMB:47;
(1GateCircStr (<*x,y*>,nor2)) +* (1GateCircStr (<*y,z*>,nor2)) tolerates 1GateCircStr (<*z,x*>,nor2) by CIRCCOMB:47;
then InnerVertices (GFA3CarryIStr (x,y,z)) = (InnerVertices ((1GateCircStr (<*x,y*>,nor2)) +* (1GateCircStr (<*y,z*>,nor2)))) \/ (InnerVertices (1GateCircStr (<*z,x*>,nor2))) by CIRCCOMB:11
.= ((InnerVertices (1GateCircStr (<*x,y*>,nor2))) \/ (InnerVertices (1GateCircStr (<*y,z*>,nor2)))) \/ (InnerVertices (1GateCircStr (<*z,x*>,nor2))) by A1, CIRCCOMB:11
.= ({[<*x,y*>,nor2]} \/ (InnerVertices (1GateCircStr (<*y,z*>,nor2)))) \/ (InnerVertices (1GateCircStr (<*z,x*>,nor2))) by CIRCCOMB:42
.= ({[<*x,y*>,nor2]} \/ {[<*y,z*>,nor2]}) \/ (InnerVertices (1GateCircStr (<*z,x*>,nor2))) by CIRCCOMB:42
.= ({[<*x,y*>,nor2]} \/ {[<*y,z*>,nor2]}) \/ {[<*z,x*>,nor2]} by CIRCCOMB:42
.= {[<*x,y*>,nor2],[<*y,z*>,nor2]} \/ {[<*z,x*>,nor2]} by ENUMSET1:1
.= {[<*x,y*>,nor2],[<*y,z*>,nor2],[<*z,x*>,nor2]} by ENUMSET1:3 ;
hence InnerVertices (GFA3CarryIStr (x,y,z)) = {[<*x,y*>,nor2],[<*y,z*>,nor2],[<*z,x*>,nor2]} ; :: thesis: verum