set f0 = xor2 ;
set f1 = and2b ;
set f2 = and2b ;
set f3 = and2b ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2 ] & x <> [<*y,z*>,and2b ] & y <> [<*z,x*>,and2b ] & z <> [<*x,y*>,and2b ] implies InputVertices (BitGFA3Str x,y,z) = {x,y,z} )
assume that
A1: z <> [<*x,y*>,xor2 ] and
A2: ( x <> [<*y,z*>,and2b ] & y <> [<*z,x*>,and2b ] & z <> [<*x,y*>,and2b ] ) ; :: thesis: InputVertices (BitGFA3Str x,y,z) = {x,y,z}
set S = BitGFA3Str x,y,z;
set S1 = GFA3AdderStr x,y,z;
set S2 = GFA3CarryStr x,y,z;
A3: InputVertices (GFA3AdderStr x,y,z) = {x,y,z} by A1, FACIRC_1:57;
InputVertices (GFA3CarryStr x,y,z) = {x,y,z} by A2, Th127;
hence InputVertices (BitGFA3Str x,y,z) = {x,y,z} by A3, CIRCCOMB:55, FACIRC_2:22; :: thesis: verum