set f1 = and2 ;
set f2 = and2 ;
set f3 = and2 ;
set f0 = xor2 ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2] & x <> [<*y,z*>,and2] & y <> [<*z,x*>,and2] & z <> [<*x,y*>,and2] implies ( x in InputVertices (BitGFA0Str (x,y,z)) & y in InputVertices (BitGFA0Str (x,y,z)) & z in InputVertices (BitGFA0Str (x,y,z)) ) )
assume A1: ( z <> [<*x,y*>,xor2] & x <> [<*y,z*>,and2] & y <> [<*z,x*>,and2] & z <> [<*x,y*>,and2] ) ; :: thesis: ( x in InputVertices (BitGFA0Str (x,y,z)) & y in InputVertices (BitGFA0Str (x,y,z)) & z in InputVertices (BitGFA0Str (x,y,z)) )
set S = BitGFA0Str (x,y,z);
InputVertices (BitGFA0Str (x,y,z)) = {x,y,z} by A1, Th33;
hence ( x in InputVertices (BitGFA0Str (x,y,z)) & y in InputVertices (BitGFA0Str (x,y,z)) & z in InputVertices (BitGFA0Str (x,y,z)) ) by ENUMSET1:def 1; :: thesis: verum