theorem :: GFACIRC1:36

for x, y, z being set holds
( x in the carrier of (BitGFA0Str (x,y,z)) & y in the carrier of (BitGFA0Str (x,y,z)) & z in the carrier of (BitGFA0Str (x,y,z)) & [<*x,y*>,xor2] in the carrier of (BitGFA0Str (x,y,z)) & [<*[<*x,y*>,xor2],z*>,xor2] in the carrier of (BitGFA0Str (x,y,z)) & [<*x,y*>,and2] in the carrier of (BitGFA0Str (x,y,z)) & [<*y,z*>,and2] in the carrier of (BitGFA0Str (x,y,z)) & [<*z,x*>,and2] in the carrier of (BitGFA0Str (x,y,z)) & [<*[<*x,y*>,and2],[<*y,z*>,and2],[<*z,x*>,and2]*>,or3] in the carrier of (BitGFA0Str (x,y,z)) )