let x, y, z be set ; :: thesis: for p being set holds GFA2AdderOutput (x,y,z) <> [p,and2a]
let p be set ; :: thesis: GFA2AdderOutput (x,y,z) <> [p,and2a]
set A1 = GFA2AdderOutput (x,y,z);

now

assume [p,and2a] `2 = (GFA2AdderOutput (x,y,z)) `2 ; :: thesis: contradiction
then A1: [p,and2a] `2 = xor2c by MCART_1:7;
[p,and2a] `2 = and2a by MCART_1:7;
hence contradiction by A1, GFACIRC1:4, TWOSCOMP:9; :: thesis: verum

end;

hence GFA2AdderOutput (x,y,z) <> [p,and2a] ; :: thesis: verum