Local Open Scope nat.
Definition LBLOCK : nat := Z.to_nat LBLOCKz.
Definition CBLOCK : nat := Z.to_nat CBLOCKz.
Opaque LBLOCK CBLOCK.

Theorem Zmod_mod_mult :
forall n a b, (0 < a)%Z -> (0 <= b)%Z ->
Zmod (Zmod n (a * b)) b = Zmod n b.