set f = xor2c ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2c ] implies ( x in InputVertices (GFA1AdderStr x,y,z) & y in InputVertices (GFA1AdderStr x,y,z) & z in InputVertices (GFA1AdderStr x,y,z) ) )
assume A1: z <> [<*x,y*>,xor2c ] ; :: thesis: ( x in InputVertices (GFA1AdderStr x,y,z) & y in InputVertices (GFA1AdderStr x,y,z) & z in InputVertices (GFA1AdderStr x,y,z) )
set S = GFA1AdderStr x,y,z;
InputVertices (GFA1AdderStr x,y,z) = {x,y,z} by A1, FACIRC_1:57;
hence ( x in InputVertices (GFA1AdderStr x,y,z) & y in InputVertices (GFA1AdderStr x,y,z) & z in InputVertices (GFA1AdderStr x,y,z) ) by ENUMSET1:def 1; :: thesis: verum