set f0 = xor2 ;
set f1 = and2 ;
set f2 = and2 ;
set f3 = and2 ;
let x, y, z be set ; :: thesis: InnerVertices (BitGFA0Str x,y,z) = (({[<*x,y*>,xor2 ]} \/ {(GFA0AdderOutput x,y,z)}) \/ {[<*x,y*>,and2 ],[<*y,z*>,and2 ],[<*z,x*>,and2 ]}) \/ {(GFA0CarryOutput x,y,z)}
set xyf0 = [<*x,y*>,xor2 ];
set xyf1 = [<*x,y*>,and2 ];
set yzf2 = [<*y,z*>,and2 ];
set zxf3 = [<*z,x*>,and2 ];
set S = BitGFA0Str x,y,z;
set S1 = GFA0AdderStr x,y,z;
set S2 = GFA0CarryStr x,y,z;
set A1 = GFA0AdderOutput x,y,z;
set A2 = GFA0CarryOutput x,y,z;
thus InnerVertices (BitGFA0Str x,y,z) = (InnerVertices (GFA0AdderStr x,y,z)) \/ (InnerVertices (GFA0CarryStr x,y,z)) by FACIRC_1:27
.= ({[<*x,y*>,xor2 ]} \/ {(GFA0AdderOutput x,y,z)}) \/ (InnerVertices (GFA0CarryStr x,y,z)) by Th27
.= ({[<*x,y*>,xor2 ]} \/ {(GFA0AdderOutput x,y,z)}) \/ ({[<*x,y*>,and2 ],[<*y,z*>,and2 ],[<*z,x*>,and2 ]} \/ {(GFA0CarryOutput x,y,z)}) by Th14
.= (({[<*x,y*>,xor2 ]} \/ {(GFA0AdderOutput x,y,z)}) \/ {[<*x,y*>,and2 ],[<*y,z*>,and2 ],[<*z,x*>,and2 ]}) \/ {(GFA0CarryOutput x,y,z)} by XBOOLE_1:4 ; :: thesis: verum