let x, y, z be set ; :: thesis: InnerVertices (BitGFA2Str x,y,z) = (({[<*x,y*>,xor2c ]} \/ {(GFA2AdderOutput x,y,z)}) \/ {[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]}) \/ {(GFA2CarryOutput x,y,z)}
set f1 = and2a ;
set f2 = and2c ;
set f3 = and2b ;
set f0 = xor2c ;
set xyf0 = [<*x,y*>,xor2c ];
set xyf1 = [<*x,y*>,and2a ];
set yzf2 = [<*y,z*>,and2c ];
set zxf3 = [<*z,x*>,and2b ];
set S = BitGFA2Str x,y,z;
set S1 = GFA2AdderStr x,y,z;
set S2 = GFA2CarryStr x,y,z;
set A1 = GFA2AdderOutput x,y,z;
set A2 = GFA2CarryOutput x,y,z;
thus InnerVertices (BitGFA2Str x,y,z) = (InnerVertices (GFA2AdderStr x,y,z)) \/ (InnerVertices (GFA2CarryStr x,y,z)) by FACIRC_1:27
.= ({[<*x,y*>,xor2c ]} \/ {(GFA2AdderOutput x,y,z)}) \/ (InnerVertices (GFA2CarryStr x,y,z)) by Th100
.= ({[<*x,y*>,xor2c ]} \/ {(GFA2AdderOutput x,y,z)}) \/ ({[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]} \/ {(GFA2CarryOutput x,y,z)}) by Th87
.= (({[<*x,y*>,xor2c ]} \/ {(GFA2AdderOutput x,y,z)}) \/ {[<*x,y*>,and2a ],[<*y,z*>,and2c ],[<*z,x*>,and2b ]}) \/ {(GFA2CarryOutput x,y,z)} by XBOOLE_1:4 ; :: thesis: verum