+
+(*
+theorem is_positive_denominator_Qinv:
+ ∀q. is_positive q → enumerator q = denominator (Qinv q).
+ intro;
+ elim q;
+ [1,3: elim H;
+ | simplify; clear H;
+ elim r; simplify;
+ [ reflexivity
+ | rewrite > denominator_integral_factor_finv;
+ reflexivity]]
+qed.
+
+theorem is_negative_denominator_Qinv:
+ ∀q. is_negative q → enumerator q = -(denominator (Qinv q)).
+ intro;
+ elim q;
+ [1,2: elim H;
+ | simplify; clear H;
+ elim r; simplify;
+ [ reflexivity
+ | rewrite > denominator_integral_factor_finv;
+ unfold Zopp;
+ elim (denominator_integral_fraction (finv f));
+ simplify;
+ [ reflexivity
+ | generalize in match (lt_O_defactorize_aux (nat_fact_of_integral_fraction a) O);
+ elim (defactorize_aux (nat_fact_of_integral_fraction a) O);
+ simplify;
+ [ elim (Not_lt_n_n ? H)
+ | reflexivity]]]]
+qed.
+
+theorem is_positive_enumerator_Qinv:
+ ∀q. is_positive q → enumerator (Qinv q) = denominator q.
+ intros;
+ lapply (is_positive_denominator_Qinv (Qinv q));
+ [ rewrite > Qinv_Qinv in Hletin;
+ assumption
+ | elim q in H ⊢ %; assumption]
+qed.
+
+theorem is_negative_enumerator_Qinv:
+ ∀q. is_negative q → enumerator (Qinv q) = -(denominator q).
+ intros;
+ lapply (is_negative_denominator_Qinv (Qinv q));
+ [ rewrite > Qinv_Qinv in Hletin;
+ assumption
+ | elim q in H ⊢ %; assumption]
+qed.
+*)
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