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;

now

assume [p,and2c ] `2 = (GFA1AdderOutput x,y,z) `2 ; :: thesis: contradiction
then A1: [p,and2c ] `2 = xor2c by MCART_1:7;
[p,and2c ] `2 = and2c by MCART_1:7;
hence contradiction by A1, GFACIRC1:3, GFACIRC1:4; :: thesis: verum

end;

hence GFA1AdderOutput x,y,z <> [p,and2c ] ; :: thesis: verum