set f = xor2c ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2c ] implies ( x in InputVertices (GFA2AdderStr x,y,z) & y in InputVertices (GFA2AdderStr x,y,z) & z in InputVertices (GFA2AdderStr x,y,z) ) )
assume A1: z <> [<*x,y*>,xor2c ] ; :: thesis: ( x in InputVertices (GFA2AdderStr x,y,z) & y in InputVertices (GFA2AdderStr x,y,z) & z in InputVertices (GFA2AdderStr x,y,z) )
set S1 = GFA1AdderStr x,y,z;
GFA2AdderStr x,y,z = GFA1AdderStr x,y,z ;
hence ( x in InputVertices (GFA2AdderStr x,y,z) & y in InputVertices (GFA2AdderStr x,y,z) & z in InputVertices (GFA2AdderStr x,y,z) ) by A1, Th69; :: thesis: verum