set f1 = and2b ;
set f2 = and2b ;
set f3 = and2b ;
set f0 = xor2 ;
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 A1: ( z <> [<*x,y*>,xor2] & x <> [<*y,z*>,and2b] & y <> [<*z,x*>,and2b] & z <> [<*x,y*>,and2b] ) ; :: thesis: InputVertices (BitGFA3Str (x,y,z)) = {x,y,z}
set S2 = GFA3CarryStr (x,y,z);
set S1 = GFA3AdderStr (x,y,z);
( InputVertices (GFA3AdderStr (x,y,z)) = {x,y,z} & InputVertices (GFA3CarryStr (x,y,z)) = {x,y,z} ) by A1, Th127, FACIRC_1:57;
hence InputVertices (BitGFA3Str (x,y,z)) = {x,y,z} by CIRCCOMB:47, FACIRC_2:21; :: thesis: verum