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-rw-r--r--CHANGES1
-rw-r--r--doc/refman/RefMan-pro.tex8
-rw-r--r--parsing/g_proofs.ml430
-rw-r--r--plugins/rtauto/Rtauto.v225
-rw-r--r--theories/Reals/Ranalysis5.v62
5 files changed, 168 insertions, 158 deletions
diff --git a/CHANGES b/CHANGES
index 2ad4b87f4..0e80215fd 100644
--- a/CHANGES
+++ b/CHANGES
@@ -63,6 +63,7 @@ Focusing
- Focusing bracket `{` now supports single-numbered goal selector,
e.g. `2: {` will focus on the second sub-goal. As usual, unfocus
with `}` once the sub-goal is fully solved.
+ The `Focus` and `Unfocus` commands are now deprecated.
Vernacular Commands
diff --git a/doc/refman/RefMan-pro.tex b/doc/refman/RefMan-pro.tex
index 6b24fdde7..bd74a40d7 100644
--- a/doc/refman/RefMan-pro.tex
+++ b/doc/refman/RefMan-pro.tex
@@ -298,15 +298,19 @@ subgoals which clutter your screen.
\begin{Variant}
\item {\tt Focus {\num}.}\\
This focuses the attention on the $\num^{th}$ subgoal to prove.
-
\end{Variant}
+\emph{This command is deprecated since 8.8: prefer the use of bullets or
+ focusing brackets instead, including {\tt {\num}: \{}}.
+
\subsection[\tt Unfocus.]{\tt Unfocus.\comindex{Unfocus}}
This command restores to focus the goal that were suspended by the
last {\tt Focus} command.
+\emph{This command is deprecated since 8.8.}
+
\subsection[\tt Unfocused.]{\tt Unfocused.\comindex{Unfocused}}
-Succeeds in the proof is fully unfocused, fails is there are some
+Succeeds in the proof if fully unfocused, fails if there are some
goals out of focus.
\subsection[\tt \{ \textrm{and} \}]{\tt \{ \textrm{and} \}\comindex{\{}\comindex{\}}}\label{curlybacket}
diff --git a/parsing/g_proofs.ml4 b/parsing/g_proofs.ml4
index 430d18893..e393c2bbf 100644
--- a/parsing/g_proofs.ml4
+++ b/parsing/g_proofs.ml4
@@ -21,6 +21,24 @@ let thm_token = G_vernac.thm_token
let hint = Gram.entry_create "hint"
+let warn_deprecated_focus =
+ CWarnings.create ~name:"deprecated-focus" ~category:"deprecated"
+ (fun () ->
+ Pp.strbrk
+ "The Focus command is deprecated; use bullets or focusing brackets instead"
+ )
+
+let warn_deprecated_focus_n n =
+ CWarnings.create ~name:"deprecated-focus" ~category:"deprecated"
+ (fun () ->
+ Pp.(str "The Focus command is deprecated;" ++ spc ()
+ ++ str "use '" ++ int n ++ str ": {' instead")
+ )
+
+let warn_deprecated_unfocus =
+ CWarnings.create ~name:"deprecated-unfocus" ~category:"deprecated"
+ (fun () -> Pp.strbrk "The Unfocus command is deprecated")
+
(* Proof commands *)
GEXTEND Gram
GLOBAL: hint command;
@@ -51,9 +69,15 @@ GEXTEND Gram
| IDENT "Undo" -> VernacUndo 1
| IDENT "Undo"; n = natural -> VernacUndo n
| IDENT "Undo"; IDENT "To"; n = natural -> VernacUndoTo n
- | IDENT "Focus" -> VernacFocus None
- | IDENT "Focus"; n = natural -> VernacFocus (Some n)
- | IDENT "Unfocus" -> VernacUnfocus
+ | IDENT "Focus" ->
+ warn_deprecated_focus ~loc:!@loc ();
+ VernacFocus None
+ | IDENT "Focus"; n = natural ->
+ warn_deprecated_focus_n n ~loc:!@loc ();
+ VernacFocus (Some n)
+ | IDENT "Unfocus" ->
+ warn_deprecated_unfocus ~loc:!@loc ();
+ VernacUnfocus
| IDENT "Unfocused" -> VernacUnfocused
| IDENT "Show" -> VernacShow (ShowGoal OpenSubgoals)
| IDENT "Show"; n = natural -> VernacShow (ShowGoal (NthGoal n))
diff --git a/plugins/rtauto/Rtauto.v b/plugins/rtauto/Rtauto.v
index 19b3ab397..06cdf76b4 100644
--- a/plugins/rtauto/Rtauto.v
+++ b/plugins/rtauto/Rtauto.v
@@ -255,122 +255,115 @@ Theorem interp_proof:
forall p hyps F gl,
check_proof hyps gl p = true -> interp_ctx hyps F [[gl]].
-induction p;intros hyps F gl.
-
-(* cas Axiom *)
-Focus 1.
-simpl;case_eq (get p hyps);clean.
-intros f nth_f e;rewrite <- (form_eq_refl e).
-apply project with p;trivial.
-
-(* Cas Arrow_Intro *)
-Focus 1.
-destruct gl;clean.
-simpl;intros.
-change (interp_ctx (hyps\gl1) (F_push gl1 hyps F) [[gl2]]).
-apply IHp;try constructor;trivial.
-
-(* Cas Arrow_Elim *)
-Focus 1.
-simpl check_proof;case_eq (get p hyps);clean.
-intros f ef;case_eq (get p0 hyps);clean.
-intros f0 ef0;destruct f0;clean.
-case_eq (form_eq f f0_1);clean.
-simpl;intros e check_p1.
-generalize (project F ef) (project F ef0)
-(IHp (hyps \ f0_2) (F_push f0_2 hyps F) gl check_p1);
-clear check_p1 IHp p p0 p1 ef ef0.
-simpl.
-apply compose3.
-rewrite (form_eq_refl e).
-auto.
-
-(* cas Arrow_Destruct *)
-Focus 1.
-simpl;case_eq (get p1 hyps);clean.
-intros f ef;destruct f;clean.
-destruct f1;clean.
-case_eq (check_proof (hyps \ f1_2 =>> f2 \ f1_1) f1_2 p2);clean.
-intros check_p1 check_p2.
-generalize (project F ef)
-(IHp1 (hyps \ f1_2 =>> f2 \ f1_1)
-(F_push f1_1 (hyps \ f1_2 =>> f2)
- (F_push (f1_2 =>> f2) hyps F)) f1_2 check_p1)
-(IHp2 (hyps \ f2) (F_push f2 hyps F) gl check_p2).
-simpl;apply compose3;auto.
-
-(* Cas False_Elim *)
-Focus 1.
-simpl;case_eq (get p hyps);clean.
-intros f ef;destruct f;clean.
-intros _; generalize (project F ef).
-apply compose1;apply False_ind.
-
-(* Cas And_Intro *)
-Focus 1.
-simpl;destruct gl;clean.
-case_eq (check_proof hyps gl1 p1);clean.
-intros Hp1 Hp2;generalize (IHp1 hyps F gl1 Hp1) (IHp2 hyps F gl2 Hp2).
-apply compose2 ;simpl;auto.
-
-(* cas And_Elim *)
-Focus 1.
-simpl;case_eq (get p hyps);clean.
-intros f ef;destruct f;clean.
-intro check_p;generalize (project F ef)
-(IHp (hyps \ f1 \ f2) (F_push f2 (hyps \ f1) (F_push f1 hyps F)) gl check_p).
-simpl;apply compose2;intros [h1 h2];auto.
-
-(* cas And_Destruct *)
-Focus 1.
-simpl;case_eq (get p hyps);clean.
-intros f ef;destruct f;clean.
-destruct f1;clean.
-intro H;generalize (project F ef)
-(IHp (hyps \ f1_1 =>> f1_2 =>> f2)
-(F_push (f1_1 =>> f1_2 =>> f2) hyps F) gl H);clear H;simpl.
-apply compose2;auto.
-
-(* cas Or_Intro_left *)
-Focus 1.
-destruct gl;clean.
-intro Hp;generalize (IHp hyps F gl1 Hp).
-apply compose1;simpl;auto.
-
-(* cas Or_Intro_right *)
-Focus 1.
-destruct gl;clean.
-intro Hp;generalize (IHp hyps F gl2 Hp).
-apply compose1;simpl;auto.
-
-(* cas Or_elim *)
-Focus 1.
-simpl;case_eq (get p1 hyps);clean.
-intros f ef;destruct f;clean.
-case_eq (check_proof (hyps \ f1) gl p2);clean.
-intros check_p1 check_p2;generalize (project F ef)
-(IHp1 (hyps \ f1) (F_push f1 hyps F) gl check_p1)
-(IHp2 (hyps \ f2) (F_push f2 hyps F) gl check_p2);
-simpl;apply compose3;simpl;intro h;destruct h;auto.
-
-(* cas Or_Destruct *)
-Focus 1.
-simpl;case_eq (get p hyps);clean.
-intros f ef;destruct f;clean.
-destruct f1;clean.
-intro check_p0;generalize (project F ef)
-(IHp (hyps \ f1_1 =>> f2 \ f1_2 =>> f2)
-(F_push (f1_2 =>> f2) (hyps \ f1_1 =>> f2)
- (F_push (f1_1 =>> f2) hyps F)) gl check_p0);simpl.
-apply compose2;auto.
-
-(* cas Cut *)
-Focus 1.
-simpl;case_eq (check_proof hyps f p1);clean.
-intros check_p1 check_p2;
-generalize (IHp1 hyps F f check_p1)
-(IHp2 (hyps\f) (F_push f hyps F) gl check_p2);
-simpl; apply compose2;auto.
+induction p; intros hyps F gl.
+
+- (* Axiom *)
+ simpl;case_eq (get p hyps);clean.
+ intros f nth_f e;rewrite <- (form_eq_refl e).
+ apply project with p;trivial.
+
+- (* Arrow_Intro *)
+ destruct gl; clean.
+ simpl; intros.
+ change (interp_ctx (hyps\gl1) (F_push gl1 hyps F) [[gl2]]).
+ apply IHp; try constructor; trivial.
+
+- (* Arrow_Elim *)
+ simpl check_proof; case_eq (get p hyps); clean.
+ intros f ef; case_eq (get p0 hyps); clean.
+ intros f0 ef0; destruct f0; clean.
+ case_eq (form_eq f f0_1); clean.
+ simpl; intros e check_p1.
+ generalize (project F ef) (project F ef0)
+ (IHp (hyps \ f0_2) (F_push f0_2 hyps F) gl check_p1);
+ clear check_p1 IHp p p0 p1 ef ef0.
+ simpl.
+ apply compose3.
+ rewrite (form_eq_refl e).
+ auto.
+
+- (* Arrow_Destruct *)
+ simpl; case_eq (get p1 hyps); clean.
+ intros f ef; destruct f; clean.
+ destruct f1; clean.
+ case_eq (check_proof (hyps \ f1_2 =>> f2 \ f1_1) f1_2 p2); clean.
+ intros check_p1 check_p2.
+ generalize (project F ef)
+ (IHp1 (hyps \ f1_2 =>> f2 \ f1_1)
+ (F_push f1_1 (hyps \ f1_2 =>> f2)
+ (F_push (f1_2 =>> f2) hyps F)) f1_2 check_p1)
+ (IHp2 (hyps \ f2) (F_push f2 hyps F) gl check_p2).
+ simpl; apply compose3; auto.
+
+- (* False_Elim *)
+ simpl; case_eq (get p hyps); clean.
+ intros f ef; destruct f; clean.
+ intros _; generalize (project F ef).
+ apply compose1; apply False_ind.
+
+- (* And_Intro *)
+ simpl; destruct gl; clean.
+ case_eq (check_proof hyps gl1 p1); clean.
+ intros Hp1 Hp2;generalize (IHp1 hyps F gl1 Hp1) (IHp2 hyps F gl2 Hp2).
+ apply compose2 ; simpl; auto.
+
+- (* And_Elim *)
+ simpl; case_eq (get p hyps); clean.
+ intros f ef; destruct f; clean.
+ intro check_p;
+ generalize (project F ef)
+ (IHp (hyps \ f1 \ f2) (F_push f2 (hyps \ f1) (F_push f1 hyps F)) gl check_p).
+ simpl; apply compose2; intros [h1 h2]; auto.
+
+- (* And_Destruct*)
+ simpl; case_eq (get p hyps); clean.
+ intros f ef; destruct f; clean.
+ destruct f1; clean.
+ intro H;
+ generalize (project F ef)
+ (IHp (hyps \ f1_1 =>> f1_2 =>> f2)
+ (F_push (f1_1 =>> f1_2 =>> f2) hyps F) gl H);
+ clear H; simpl.
+ apply compose2; auto.
+
+- (* Or_Intro_left *)
+ destruct gl; clean.
+ intro Hp; generalize (IHp hyps F gl1 Hp).
+ apply compose1; simpl; auto.
+
+- (* Or_Intro_right *)
+ destruct gl; clean.
+ intro Hp; generalize (IHp hyps F gl2 Hp).
+ apply compose1; simpl; auto.
+
+- (* Or_elim *)
+ simpl; case_eq (get p1 hyps); clean.
+ intros f ef; destruct f; clean.
+ case_eq (check_proof (hyps \ f1) gl p2); clean.
+ intros check_p1 check_p2;
+ generalize (project F ef)
+ (IHp1 (hyps \ f1) (F_push f1 hyps F) gl check_p1)
+ (IHp2 (hyps \ f2) (F_push f2 hyps F) gl check_p2);
+ simpl; apply compose3; simpl; intro h; destruct h; auto.
+
+- (* Or_Destruct *)
+ simpl; case_eq (get p hyps); clean.
+ intros f ef; destruct f; clean.
+ destruct f1; clean.
+ intro check_p0;
+ generalize (project F ef)
+ (IHp (hyps \ f1_1 =>> f2 \ f1_2 =>> f2)
+ (F_push (f1_2 =>> f2) (hyps \ f1_1 =>> f2)
+ (F_push (f1_1 =>> f2) hyps F)) gl check_p0);
+ simpl.
+ apply compose2; auto.
+
+- (* Cut *)
+ simpl; case_eq (check_proof hyps f p1); clean.
+ intros check_p1 check_p2;
+ generalize (IHp1 hyps F f check_p1)
+ (IHp2 (hyps\f) (F_push f hyps F) gl check_p2);
+ simpl; apply compose2; auto.
Qed.
Theorem Reflect: forall gl prf, if check_proof empty gl prf then [[gl]] else True.
diff --git a/theories/Reals/Ranalysis5.v b/theories/Reals/Ranalysis5.v
index 88ab4d6e1..afb78e1c8 100644
--- a/theories/Reals/Ranalysis5.v
+++ b/theories/Reals/Ranalysis5.v
@@ -29,46 +29,34 @@ Lemma f_incr_implies_g_incr_interv : forall f g:R->R, forall lb ub,
(forall x , f lb <= x -> x <= f ub -> lb <= g x <= ub) ->
(forall x y, f lb <= x -> x < y -> y <= f ub -> g x < g y).
Proof.
-intros f g lb ub lb_lt_ub f_incr f_eq_g g_ok x y lb_le_x x_lt_y y_le_ub.
- assert (x_encad : f lb <= x <= f ub).
- split ; [assumption | apply Rle_trans with (r2:=y) ; [apply Rlt_le|] ; assumption].
- assert (y_encad : f lb <= y <= f ub).
- split ; [apply Rle_trans with (r2:=x) ; [|apply Rlt_le] ; assumption | assumption].
- assert (Temp1 : lb <= lb) by intuition ; assert (Temp2 : ub <= ub) by intuition.
- assert (gx_encad := g_ok _ (proj1 x_encad) (proj2 x_encad)).
- assert (gy_encad := g_ok _ (proj1 y_encad) (proj2 y_encad)).
- clear Temp1 Temp2.
- case (Rlt_dec (g x) (g y)).
- intuition.
+ intros f g lb ub lb_lt_ub f_incr f_eq_g g_ok x y lb_le_x x_lt_y y_le_ub.
+ assert (x_encad : f lb <= x <= f ub) by lra.
+ assert (y_encad : f lb <= y <= f ub) by lra.
+ assert (gx_encad := g_ok _ (proj1 x_encad) (proj2 x_encad)).
+ assert (gy_encad := g_ok _ (proj1 y_encad) (proj2 y_encad)).
+ case (Rlt_dec (g x) (g y)); [ easy |].
intros Hfalse.
- assert (Temp := Rnot_lt_le _ _ Hfalse).
- assert (Hcontradiction : y <= x).
- replace y with (id y) by intuition ; replace x with (id x) by intuition ;
- rewrite <- f_eq_g. rewrite <- f_eq_g.
- assert (f_incr2 : forall x y, lb <= x -> x <= y -> y < ub -> f x <= f y).
+ assert (Temp := Rnot_lt_le _ _ Hfalse).
+ enough (y <= x) by lra.
+ replace y with (id y) by easy.
+ replace x with (id x) by easy.
+ rewrite <- f_eq_g by easy.
+ rewrite <- f_eq_g by easy.
+ assert (f_incr2 : forall x y, lb <= x -> x <= y -> y < ub -> f x <= f y). {
intros m n lb_le_m m_le_n n_lt_ub.
case (m_le_n).
- intros ; apply Rlt_le ; apply f_incr ; [| | apply Rlt_le] ; assumption.
- intros Hyp ; rewrite Hyp ; apply Req_le ; reflexivity.
- apply f_incr2.
- intuition. intuition.
- Focus 3. intuition.
- Focus 2. intuition.
- Focus 2. intuition. Focus 2. intuition.
- assert (Temp2 : g x <> ub).
- intro Hf.
- assert (Htemp : (comp f g) x = f ub).
- unfold comp ; rewrite Hf ; reflexivity.
- rewrite f_eq_g in Htemp ; unfold id in Htemp.
- assert (Htemp2 : x < f ub).
- apply Rlt_le_trans with (r2:=y) ; intuition.
- clear -Htemp Htemp2. fourier.
- intuition. intuition.
- clear -Temp2 gx_encad.
- case (proj2 gx_encad).
- intuition.
- intro Hfalse ; apply False_ind ; apply Temp2 ; assumption.
- apply False_ind. clear - Hcontradiction x_lt_y. fourier.
+ - intros; apply Rlt_le, f_incr, Rlt_le; assumption.
+ - intros Hyp; rewrite Hyp; apply Req_le; reflexivity.
+ }
+ apply f_incr2; intuition.
+ enough (g x <> ub) by lra.
+ intro Hf.
+ assert (Htemp : (comp f g) x = f ub). {
+ unfold comp; rewrite Hf; reflexivity.
+ }
+ rewrite f_eq_g in Htemp by easy.
+ unfold id in Htemp.
+ fourier.
Qed.
Lemma derivable_pt_id_interv : forall (lb ub x:R),
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-15 17:37:56 +0000