let x, y, z be set ; :: thesis: for p being set holds GFA1AdderOutput (x,y,z) <> [p,and2c]
let p be set ; :: thesis: GFA1AdderOutput (x,y,z) <> [p,and2c]
set A1 = GFA1AdderOutput (x,y,z);
(GFA1AdderOutput (x,y,z)) `2 = xor2c ;
then [p,and2c] `2 <> (GFA1AdderOutput (x,y,z)) `2 by GFACIRC1:3, GFACIRC1:4;
hence GFA1AdderOutput (x,y,z) <> [p,and2c] ; :: thesis: verum