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, Th58; :: thesis: verum