set f = xor2 ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2 ] implies for s being State of (GFA3AdderCirc x,y,z)
for a1a2, a1, a2, a3 being Element of BOOLEAN st a1a2 = s . [<*x,y*>,xor2 ] & a1 = s . x & a2 = s . y & a3 = s . z holds
(Following s) . (GFA3AdderOutput x,y,z) = a1a2 'xor' a3 )
assume A1: z <> [<*x,y*>,xor2 ] ; :: thesis: for s being State of (GFA3AdderCirc x,y,z)
for a1a2, a1, a2, a3 being Element of BOOLEAN st a1a2 = s . [<*x,y*>,xor2 ] & a1 = s . x & a2 = s . y & a3 = s . z holds
(Following s) . (GFA3AdderOutput x,y,z) = a1a2 'xor' a3
set A3 = GFA3AdderCirc x,y,z;
set A0 = GFA0AdderCirc x,y,z;
set O3 = GFA3AdderOutput x,y,z;
set O0 = GFA0AdderOutput x,y,z;
( GFA3AdderCirc x,y,z = GFA0AdderCirc x,y,z & GFA3AdderOutput x,y,z = GFA0AdderOutput x,y,z ) ;
hence for s being State of (GFA3AdderCirc x,y,z)
for a1a2, a1, a2, a3 being Element of BOOLEAN st a1a2 = s . [<*x,y*>,xor2 ] & a1 = s . x & a2 = s . y & a3 = s . z holds
(Following s) . (GFA3AdderOutput x,y,z) = a1a2 'xor' a3 by A1, Th36; :: thesis: verum