let x, y, z be set ; :: thesis: for p being set holds GFA0AdderOutput x,y,z <> [p,and2 ]
let p be set ; :: thesis: GFA0AdderOutput x,y,z <> [p,and2 ]
set A1 = GFA0AdderOutput x,y,z;

now

assume [p,and2 ] `2 = (GFA0AdderOutput x,y,z) `2 ; :: thesis: contradiction
then A1: [p,and2 ] `2 = xor2 by MCART_1:7;
[p,and2 ] `2 = and2 by MCART_1:7;
hence contradiction by A1, TWOSCOMP:11, TWOSCOMP:13; :: thesis: verum

end;

hence GFA0AdderOutput x,y,z <> [p,and2 ] ; :: thesis: verum