let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2 ] implies ( x in InputVertices (GFA3AdderStr x,y,z) & y in InputVertices (GFA3AdderStr x,y,z) & z in InputVertices (GFA3AdderStr x,y,z) ) )
assume A1: z <> [<*x,y*>,xor2 ] ; :: thesis: ( x in InputVertices (GFA3AdderStr x,y,z) & y in InputVertices (GFA3AdderStr x,y,z) & z in InputVertices (GFA3AdderStr x,y,z) )
set S0 = GFA0AdderStr x,y,z;
GFA3AdderStr x,y,z = GFA0AdderStr x,y,z ;
hence ( x in InputVertices (GFA3AdderStr x,y,z) & y in InputVertices (GFA3AdderStr x,y,z) & z in InputVertices (GFA3AdderStr x,y,z) ) by A1, Th33; :: thesis: verum