let x, y, z be set ; ( 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]
; ( 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; verum