(** Conversely, the following results need less restrictions here. *)

(* Specifications: *)
Lemma quot_quot : forall a b c, b~=0 -> c~=0 ->
(a÷b)÷c == a÷(b*c).
Lemma mod_mul_r : forall a b c, b~=0 -> c~=0 ->
a rem (b*c) == a rem b + b*((a÷b) rem c).
Lemma rem_quot: forall a b, b~=0 ->
a rem b ÷ b == 0.