proof k : A => (B => A)
proof andcomm : (A & B) => B & A
proof curry : ((A & B) => C) => (A => B => C)
proof distribandor1 : ((A & B) | C) => (A | C) & (B | C)
proof clue : (G => (C & B) | (R & H)) => (~B => S) => (R | H) => ~(G & S) => ~(R & C) => ~(B & H) => (~G)