Module Type NZAddProp (Import NZ : NZAxiomsSig')(Import NZBase : NZBaseProp NZ).
Hint Rewrite
pred_succ add_0_l add_succ_l mul_0_l mul_succ_l sub_0_r sub_succ_r : nz.
Hint Rewrite one_succ two_succ : nz'.
Ltac nzsimpl := autorewrite with nz.
Ltac nzsimpl' := autorewrite with nz nz'.
Hint Rewrite add_0_r add_succ_r : nz.
Hint Rewrite add_1_l add_1_r : nz.

Theorem add_shuffle1 : forall n m p q, (n + m) + (p + q) == (n + p) + (m + q).