Commit 39eb0a30 by Guillaume Melquiond

### Clean hypotheses.

parent 770b1646
 ... ... @@ -890,10 +890,9 @@ Proof. by apply: pow_nonzero; lra. Qed. Lemma f0eps_correct alpha beta epsilon (B : R) (Heps : 0 < / B <= epsilon) (HB : 0 < B) (Halpha : -1 < IZR alpha) : Lemma f0eps_correct alpha beta epsilon (B : R) (Heps : 0 < / B <= epsilon) (HB : 0 < B) (Halpha : (-1 < alpha)%Z) : is_RInt_gen ((fun x => powerRZ x alpha * (pow (ln x) beta))) (at_point (/ B)) (at_point epsilon) (f0eps alpha beta epsilon B). Proof. have Halpha1 : (-1 < alpha)%Z by apply: lt_IZR. have Hint : ex_RInt (fun x : R => powerRZ x alpha * ln x ^ beta) (/ B) epsilon. eexists. apply: f_correct => // . ... ... @@ -907,7 +906,7 @@ Proof. by move ->; apply: RInt_correct. rewrite -RInt_gen_at_point; last first. + eexists. apply: f_correct; try lra; try lia. + rewrite subst_lemma; try lra. + rewrite subst_lemma ; try lra. 2: now apply IZR_lt. symmetry. rewrite /f0eps. rewrite f_correct_RInt; try lra; try lia. rewrite (RInt_ext _ (fun x : R => scal (- (-1) ^ beta) (powerRZ x (-2 - alpha) * ln x ^ beta))); last first. ... ... @@ -918,7 +917,7 @@ Proof. by eexists; apply: f_correct; first (split; field_simplify; lra); lia. Qed. Lemma f0eps_correct_sing alpha beta epsilon sing (B : R) (Heps : 0 < / B <= epsilon) (HB : 0 < B) (Halpha : -1 < IZR alpha) : Lemma f0eps_correct_sing alpha beta epsilon sing (B : R) (Heps : 0 < / B <= epsilon) (HB : 0 < B) (Halpha : (-1 < alpha)%Z) : is_RInt_gen ((fun x => powerRZ (x - sing) alpha * (pow (ln (x - sing)) beta))) (at_point (sing + / B)) (at_point (sing + epsilon)) (f0eps alpha beta epsilon B). Proof. apply is_RInt_gen_at_point. ... ... @@ -928,7 +927,7 @@ Proof. rewrite !H; apply f0eps_correct => // . Qed. Lemma f0eps_lim_is_lim alpha beta epsilon (Halpha : -1 < IZR alpha) (Heps : 0 < epsilon) : Lemma f0eps_lim_is_lim alpha beta epsilon (Halpha : (-1 < alpha)%Z) (Heps : 0 < epsilon) : filterlim (fun x : R => f0eps alpha beta epsilon (/ x)) (at_right 0) (locally (f0eps_lim alpha beta epsilon)). Proof. ... ... @@ -944,11 +943,10 @@ apply: filterlim_ext. apply: is_lim_mult => // . + exact: is_lim_const. + apply: f_lim_is_lim; first exact: Rinv_0_lt_compat. have Halpha1 : (-1 < alpha)%Z by apply: lt_IZR. by lia. Qed. Lemma f0eps_lim_is_lim_sing alpha beta epsilon sing (Halpha : -1 < IZR alpha) (Heps : 0 < epsilon) : Lemma f0eps_lim_is_lim_sing alpha beta epsilon sing (Halpha : (-1 < alpha)%Z) (Heps : 0 < epsilon) : filterlim (fun x : R => f0eps alpha beta epsilon (/ (x - sing))) (at_right sing) (locally (f0eps_lim alpha beta epsilon)). Proof. ... ... @@ -963,7 +961,7 @@ Proof. exact: f0eps_lim_is_lim. Qed. Lemma f0eps_lim_correct alpha beta epsilon (Halpha : -1 < IZR alpha) (Heps : 0 < epsilon) : Lemma f0eps_lim_correct alpha beta epsilon (Halpha : (-1 < alpha)%Z) (Heps : 0 < epsilon) : is_RInt_gen ((fun x => powerRZ x alpha * (pow (ln x) beta))) (at_right 0) (at_point epsilon) (f0eps_lim alpha beta epsilon). Proof. set eps := mkposreal epsilon Heps. ... ... @@ -975,10 +973,11 @@ apply: (filterlimi_lim_ext_loc (fun x => f0eps alpha beta epsilon (/ x))). rewrite -is_RInt_gen_at_point. apply (f0eps_correct); rewrite ?Rinv_involutive; try lra. exact: Rinv_0_lt_compat. exact Halpha. exact: f0eps_lim_is_lim. Qed. Lemma f0eps_lim_correct_sing alpha beta epsilon sing (Halpha : -1 < IZR alpha) (Heps : 0 < epsilon) : Lemma f0eps_lim_correct_sing alpha beta epsilon sing (Halpha : (-1 < alpha)%Z) (Heps : 0 < epsilon) : is_RInt_gen ((fun x => powerRZ (x - sing) alpha * (pow (ln (x - sing)) beta))) (at_right sing) (at_point (sing + epsilon)) (f0eps_lim alpha beta epsilon). Proof. set eps := mkposreal epsilon Heps. ... ... @@ -990,6 +989,7 @@ apply: (filterlimi_lim_ext_loc (fun x => f0eps alpha beta epsilon (/ (x - sing)) rewrite -is_RInt_gen_at_point. apply f0eps_correct_sing; rewrite ?Rinv_involutive; try lra. apply: Rinv_0_lt_compat; lra. exact Halpha. exact: f0eps_lim_is_lim_sing. Qed. ... ...
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