set f1 = and2a ;
set f2 = and2c ;
set f3 = and2b ;
set f0 = xor2c ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2c ] & x <> [<*y,z*>,and2c ] & y <> [<*z,x*>,and2b ] & z <> [<*x,y*>,and2a ] implies InputVertices (BitGFA2Str x,y,z) = {x,y,z} )
assume A1: ( z <> [<*x,y*>,xor2c ] & x <> [<*y,z*>,and2c ] & y <> [<*z,x*>,and2b ] & z <> [<*x,y*>,and2a ] ) ; :: thesis: InputVertices (BitGFA2Str x,y,z) = {x,y,z}
set S2 = GFA2CarryStr x,y,z;
set S1 = GFA2AdderStr x,y,z;
( InputVertices (GFA2AdderStr x,y,z) = {x,y,z} & InputVertices (GFA2CarryStr x,y,z) = {x,y,z} ) by A1, Th90, FACIRC_1:57;
hence InputVertices (BitGFA2Str x,y,z) = {x,y,z} by CIRCCOMB:55, FACIRC_2:22; :: thesis: verum
set S = BitGFA2Str x,y,z;