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, Th27; :: thesis: verum