let x, y, z be set ; for p being set holds GFA2AdderOutput (x,y,z) <> [p,and2a]
let p be set ; GFA2AdderOutput (x,y,z) <> [p,and2a]
set A1 = GFA2AdderOutput (x,y,z);
(GFA2AdderOutput (x,y,z)) `2 = xor2c
;
then
[p,and2a] `2 <> (GFA2AdderOutput (x,y,z)) `2
by GFACIRC1:4, TWOSCOMP:9;
hence
GFA2AdderOutput (x,y,z) <> [p,and2a]
; verum