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Definition mult_eq := f_equal2 mult.
Definition minus_eq := f_equal2 minus.

Lemma mult_eq_Sn : forall a b : nat, 0 < b -> a * b = b -> a = 1.
Inductive is_div : nat -> nat -> nat -> nat -> Prop :=
is_div_def :
forall a b q r : nat, r < b -> a = q * b + r -> is_div a b q r.