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