exercises ready

diff --git a/helm/software/matita/library/didactic/exercises/natural_deduction.ma b/helm/software/matita/library/didactic/exercises/natural_deduction.ma
index 98142db2fd7f19ea8462c81839918798f538f8c2..5e71888149f9047fcab44fe45da3a8a8798e9c56 100644 (file)
--- a/helm/software/matita/library/didactic/exercises/natural_deduction.ma
+++ b/helm/software/matita/library/didactic/exercises/natural_deduction.ma
@@ -29,6 +29,18 @@ Per digitare i connettivi logici:
 * `⊥` : `\bot`
 * `⊤` : `\top`
 
+I termini, le formule e i nomi delle ipotesi
+============================================
+
+* I termini quantificati da `∀` e `∃`, quando argomenti di
+  una regola, vengono scritti tra `{` e `}`.
+
+* Le formule, quando argomenti di
+  una regola, vengono scritti tra `(` e `)`.
+
+* I nomi delle ipotesi, quando argomenti di
+  una regola, vengono scritti tra `[` e `]`.
+
 Le regole di deduzione naturale
 ===============================
 
@@ -75,7 +87,7 @@ DOCEND*)
 
 include "didactic/support/natural_deduction.ma".
 
-theorem EM: ∀A. A ∨ ¬ A.
+theorem EM: ∀A:CProp. A ∨ ¬ A.
 (* Il comando assume è necessario perchè dimostriamo A∨¬A
    per una A generica. *)
 assume A: CProp.

diff --git a/helm/software/matita/library/didactic/support/natural_deduction.ma b/helm/software/matita/library/didactic/support/natural_deduction.ma
index 90ebd7217751b6ab807fde4fc0b562307a6359ff..84fbeee781a535621476e798224d1c662cce5a81 100644 (file)
--- a/helm/software/matita/library/didactic/support/natural_deduction.ma
+++ b/helm/software/matita/library/didactic/support/natural_deduction.ma
@@ -45,6 +45,21 @@ definition Discharge := λA:CProp.λa:A.
 
 axiom Raa : ∀A.(Not A → Bot) → A.
 
+axiom sort : Type.
+
+inductive Exists (A:Type) (P:A→CProp) : CProp ≝
+  Exists_intro: ∀w:A. P w → Exists A P.
+
+definition Exists_elim ≝
+  λA:Type.λP:A→CProp.λC:CProp.λc:Exists A P.λH:(Πx.P x → C).
+   match c with [ Exists_intro w p ⇒ H w p ].
+
+inductive Forall (A:Type) (P:A→CProp) : CProp ≝
+ Forall_intro: (∀n:A. P n) → Forall A P.
+
+definition Forall_elim ≝
+ λA:Type.λP:A→CProp.λn:A.λf:Forall A P.match f with [ Forall_intro g ⇒ g n ].
+
 (* Dummy proposition *)
 axiom unit : CProp.
 
@@ -61,7 +76,17 @@ interpretation "Bot" 'Bot = Bot.
 interpretation "Not" 'not a = (Not a).
 notation "✶" non associative with precedence 90 for @{'unit}.
 interpretation "dummy prop" 'unit = unit.
-
+notation > "\exists list1 ident x sep , . term 19 Px" with precedence 20
+for ${ fold right @{$Px} rec acc @{'myexists (λ${ident x}.$acc)} }.
+notation < "hvbox(\exists ident i break . p)" with precedence 20
+for @{ 'myexists (\lambda ${ident i} : $ty. $p) }.
+interpretation "constructive ex" 'myexists \eta.x = (Exists sort x).
+notation > "\forall ident x.break term 19 Px" with precedence 20
+for @{ 'Forall (λ${ident x}.$Px) }.
+notation < "\forall ident x.break term 19 Px" with precedence 20
+for @{ 'Forall (λ${ident x}:$tx.$Px) }.
+interpretation "Forall" 'Forall \eta.Px = (Forall _ Px).
+ 
 (* Variables *)
 axiom A : CProp.
 axiom B : CProp.
@@ -78,24 +103,20 @@ axiom L : CProp.
 axiom M : CProp.
 axiom N : CProp.
 axiom O : CProp.
-axiom P : CProp.
-axiom Q : CProp.
-axiom R : CProp.
-axiom S : CProp.
-axiom T : CProp.
-axiom U : CProp.
-axiom V : CProp.
-axiom W : CProp.
-axiom X : CProp.
-axiom Y : CProp.
-axiom Z : CProp.
+axiom P : sort →CProp.
+axiom Q : sort →CProp.
+axiom R : sort →sort →CProp.
+axiom S : sort →sort →CProp.
+axiom f : sort → sort.
+axiom g : sort → sort.
+axiom h : sort → sort → sort.
 
 (* Every formula user provided annotates its proof:
    `A` becomes `(show A ?)` *)
-definition show : ∀A.A→A ≝ λA:CProp.λa:A.a.
+definition show : ΠA.A→A ≝ λA:CProp.λa:A.a.
 
 (* When something does not fit, this daemon is used *)
-axiom cast: ∀A,B:CProp.B → A.
+axiom cast: ΠA,B:CProp.B → A.
 
 (* begin a proof: draws the root *)
 notation > "'prove' p" non associative with precedence 19 
@@ -112,7 +133,7 @@ for @{ 'leaf_ko $a $t }.
 interpretation "leaf KO" 'leaf_ko a t = (cast _ _ (show a t)).
 
 (* already proved lemma *)
-definition Lemma : ∀A.A→A ≝ λA:CProp.λa:A.a.
+definition Lemma : ΠA.A→A ≝ λA:CProp.λa:A.a.
 
 notation < "\infrule \nbsp p mstyle color #ff0000 (\lem\emsp H)" non associative with precedence 19
 for @{ 'lemma_ko_1 $p $H }.
@@ -517,54 +538,119 @@ for @{ 'Raa (λ${ident H}.show $b ?) }.
 interpretation "RAA KO" 'Raa p = (cast _ unit (Raa _ (cast _ (unit_to _) p))).
 interpretation "RAA OK" 'Raa p = (Raa _ p).
 
-(*DOCBEGIN
-Templates for rules:
-
-        apply rule (⇒_i […] (…)).
-
-        apply rule (∧_i (…) (…));
-               [
-               |
-               ]
-
-        apply rule (∨_i_l (…)).
-
-        apply rule (∨_i_r (…)).
-
-        apply rule (¬_i […] (…)).
-
-        apply rule (⊤_i).
-
-        apply rule (⇒_e (…) (…));
-               [
-               |
-               ]
-
-        apply rule (∧_e_l (…)).
-
-        apply rule (∧_e_r (…)).
-
-        apply rule (∨_e (…) […] (…) […] (…));
-               [
-               |
-               |
-               ]
-
-        apply rule (¬_e (…) (…));
-               [
-               |
-               ]
-
-        apply rule (⊥_e (…)).
-
-        apply rule (prove (…)).
-
-        apply rule (RAA […] (…)).
-
-        apply rule (discharge […]).
-
-DOCEND*)
-
-
-
-
+(* ∃ introduction *)
+notation < "\infrule hbox(\emsp Pn \emsp) Px mstyle color #ff0000 (∃\sub\i)" with precedence 19
+for @{ 'Exists_intro_ko_1 $Pn $Px }.
+interpretation "Exists_intro_ko_1" 'Exists_intro_ko_1 Pn Px = 
+  (show Px (cast _ _ (Exists_intro _ _ _ (cast _ _ Pn)))).
+
+notation < "\infrule hbox(\emsp Pn \emsp) mstyle color #ff0000 (Px) mstyle color #ff0000 (∃\sub\i)" with precedence 19
+for @{ 'Exists_intro_ko_2 $Pn $Px }.
+interpretation "Exists_intro_ko_2" 'Exists_intro_ko_2 Pn Px = 
+  (cast _ _ (show Px (cast _ _ (Exists_intro _ _ _ (cast _ _ Pn))))).
+
+notation < "\infrule hbox(\emsp Pn \emsp) Px (∃\sub\i)" with precedence 19
+for @{ 'Exists_intro_ok_1 $Pn $Px }.
+interpretation "Exists_intro_ok_1" 'Exists_intro_ok_1 Pn Px = 
+  (show Px (Exists_intro _ _ _ Pn)).
+
+notation < "\infrule hbox(\emsp Pn \emsp) mstyle color #ff0000 (Px) (∃\sub\i)" with precedence 19
+for @{ 'Exists_intro_ok_2 $Pn $Px }.
+interpretation "Exists_intro_ok_2" 'Exists_intro_ok_2 Pn Px = 
+  (cast _ _ (show Px (Exists_intro _ _ _ Pn))).
+
+notation >"∃_'i' {term 90 t} term 90 Pt" non associative with precedence 19
+for @{'Exists_intro $t (λ_.?) (show $Pt ?)}. 
+interpretation "Exists_intro KO" 'Exists_intro t P Pt =
+ (cast _ _ (Exists_intro sort P t (cast _ _ Pt))).
+interpretation "Exists_intro OK" 'Exists_intro t P Pt =
+ (Exists_intro sort P t Pt).
+ 
+(* ∃ elimination *)
+notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) c (mstyle color #ff0000 (∃\sub\e) \emsp ident n \emsp ident HPn)" with precedence 19
+for @{ 'Exists_elim_ko_1 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
+interpretation "Exists_elim_ko_1" 'Exists_elim_ko_1 ExPx Pc c =
+    (show c (cast _ _ (Exists_elim _ _ _ (cast _ _ ExPx) (cast _ _ Pc)))).
+
+notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) mstyle color #ff0000 (c) (mstyle color #ff0000 (∃\sub\e) \emsp ident n \emsp ident HPn)" with precedence 19
+for @{ 'Exists_elim_ko_2 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
+interpretation "Exists_elim_ko_2" 'Exists_elim_ko_2 ExPx Pc c =
+    (cast _ _ (show c (cast _ _ (Exists_elim _ _ _ (cast _ _ ExPx) (cast _ _ Pc))))).
+
+notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) c (∃\sub\e \emsp ident n \emsp ident HPn)" with precedence 19
+for @{ 'Exists_elim_ok_1 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
+interpretation "Exists_elim_ok_1" 'Exists_elim_ok_1 ExPx Pc c =
+    (show c (Exists_elim _ _ _ ExPx Pc)).
+
+notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) mstyle color #ff0000 (c) (∃\sub\e \emsp ident n \emsp ident HPn)" with precedence 19
+for @{ 'Exists_elim_ok_2 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
+interpretation "Exists_elim_ok_2" 'Exists_elim_ok_2 ExPx Pc c =
+    (cast _ _ (show c (Exists_elim _ _ _ ExPx Pc))).
+
+definition ex_concl := λx:CProp.sort → unit → x.
+definition fake_pred := λx:sort.unit.
+
+notation >"∃_'e' term 90 ExPt {ident t} [ident H] term 90 c" non associative with precedence 19
+for @{'Exists_elim (λ_.?) (show $ExPt ?) (λ${ident t}:sort.λ${ident H}.show $c ?)}. 
+interpretation "Exists_elim KO" 'Exists_elim P ExPt c =
+ (cast _ _ (Exists_elim sort P _ 
+   (cast (Exists _ P)  _ ExPt) (cast (ex_concl unit) (ex_concl _) c))).
+interpretation "Exists_elim OK" 'Exists_elim P ExPt c =
+ (Exists_elim sort P _ ExPt c).
+
+(* ∀ introduction *)
+
+notation < "\infrule hbox(\emsp Px \emsp) Pn (mstyle color #ff0000 (∀\sub\i) \emsp ident x)" with precedence 19
+for @{ 'Forall_intro_ko_1 (λ${ident x}:$tx.$Px) $Pn }.
+interpretation "Forall_intro_ko_1" 'Forall_intro_ko_1 Px Pn = 
+  (show Pn (cast _ _ (Forall_intro _ _ (cast _ _ Px)))).
+
+notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000(Pn) (mstyle color #ff0000 (∀\sub\i) \emsp ident x)" with precedence 19
+for @{ 'Forall_intro_ko_2 (λ${ident x}:$tx.$Px) $Pn }.
+interpretation "Forall_intro_ko_2" 'Forall_intro_ko_2 Px Pn = 
+  (cast _ _ (show Pn (cast _ _ (Forall_intro _ _ (cast _ _ Px))))).
+
+notation < "\infrule hbox(\emsp Px \emsp) Pn (∀\sub\i \emsp ident x)" with precedence 19
+for @{ 'Forall_intro_ok_1 (λ${ident x}:$tx.$Px) $Pn }.
+interpretation "Forall_intro_ok_1" 'Forall_intro_ok_1 Px Pn = 
+  (show Pn (Forall_intro _ _ Px)).
+
+notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (∀\sub\i \emsp ident x)" with precedence 19
+for @{ 'Forall_intro_ok_2 (λ${ident x}:$tx.$Px) $Pn }.
+interpretation "Forall_intro_ok_2" 'Forall_intro_ok_2 Px Pn = 
+  (cast _ _ (show Pn (Forall_intro _ _ Px))).
+
+notation > "∀_'i' {ident y} term 90 Px" non associative with precedence 19
+for @{ 'Forall_intro (λ_.?) (λ${ident y}.show $Px ?) }. 
+interpretation "Forall_intro KO" 'Forall_intro P Px =
+  (cast _ _ (Forall_intro sort P (cast _ _ Px))). 
+interpretation "Forall_intro OK" 'Forall_intro P Px =
+  (Forall_intro sort P Px). 
+
+(* ∀ elimination *)
+notation < "\infrule hbox(\emsp Px \emsp) Pn (mstyle color #ff0000 (∀\sub\e))" with precedence 19
+for @{ 'Forall_elim_ko_1 $Px $Pn }.
+interpretation "Forall_elim_ko_1" 'Forall_elim_ko_1 Px Pn = 
+  (show Pn (cast _ _ (Forall_elim _ _ _ (cast _ _ Px)))).
+
+notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000(Pn) (mstyle color #ff0000 (∀\sub\e))" with precedence 19
+for @{ 'Forall_elim_ko_2 $Px $Pn }.
+interpretation "Forall_elim_ko_2" 'Forall_elim_ko_2 Px Pn = 
+  (cast _ _ (show Pn (cast _ _ (Forall_elim _ _ _ (cast _ _ Px))))).
+
+notation < "\infrule hbox(\emsp Px \emsp) Pn (∀\sub\e)" with precedence 19
+for @{ 'Forall_elim_ok_1 $Px $Pn }.
+interpretation "Forall_elim_ok_1" 'Forall_elim_ok_1 Px Pn = 
+  (show Pn (Forall_elim _ _ _ Px)).
+
+notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (∀\sub\e)" with precedence 19
+for @{ 'Forall_elim_ok_2 $Px $Pn }.
+interpretation "Forall_elim_ok_2" 'Forall_elim_ok_2 Px Pn = 
+  (cast _ _ (show Pn (Forall_elim _ _ _ Px))).
+
+notation > "∀_'e' {term 90 t} term 90 Pn" non associative with precedence 19
+for @{ 'Forall_elim (λ_.?) $t (show $Pn ?) }. 
+interpretation "Forall_elim KO" 'Forall_elim P t Px =
+  (cast _ unit (Forall_elim sort P t (cast _ _ Px))). 
+interpretation "Forall_elim OK" 'Forall_elim P t Px =
+  (Forall_elim sort P t Px). 

diff --git a/helm/software/matita/matita.glade b/helm/software/matita/matita.glade
index a14858d9109cdf8381fa57947a395e70a961c8e2..4739e14f80ee6a30c4688776d99699bb5a7b16de 100644 (file)
--- a/helm/software/matita/matita.glade
+++ b/helm/software/matita/matita.glade
@@ -1472,6 +1472,30 @@
                                             <property name="position">5</property>
                                           </packing>
                                         </child>
+                                        <child>
+                                          <widget class="GtkButton" id="butForall_intro">
+                                            <property name="visible">True</property>
+                                            <property name="can_focus">True</property>
+                                            <property name="receives_default">True</property>
+                                            <property name="label" translatable="yes">Universal (∀_i)</property>
+                                            <property name="response_id">0</property>
+                                          </widget>
+                                          <packing>
+                                            <property name="position">6</property>
+                                          </packing>
+                                        </child>
+                                        <child>
+                                          <widget class="GtkButton" id="butExists_intro">
+                                            <property name="visible">True</property>
+                                            <property name="can_focus">True</property>
+                                            <property name="receives_default">True</property>
+                                            <property name="label" translatable="yes">Existential (∃_i)</property>
+                                            <property name="response_id">0</property>
+                                          </widget>
+                                          <packing>
+                                            <property name="position">7</property>
+                                          </packing>
+                                        </child>
                                       </widget>
                                     </child>
                                     <child>
@@ -1564,6 +1588,30 @@
                                             <property name="position">5</property>
                                           </packing>
                                         </child>
+                                        <child>
+                                          <widget class="GtkButton" id="butForall_elim">
+                                            <property name="visible">True</property>
+                                            <property name="can_focus">True</property>
+                                            <property name="receives_default">True</property>
+                                            <property name="label" translatable="yes">Universal (∀_e)</property>
+                                            <property name="response_id">0</property>
+                                          </widget>
+                                          <packing>
+                                            <property name="position">6</property>
+                                          </packing>
+                                        </child>
+                                        <child>
+                                          <widget class="GtkButton" id="butExists_elim">
+                                            <property name="visible">True</property>
+                                            <property name="can_focus">True</property>
+                                            <property name="receives_default">True</property>
+                                            <property name="label" translatable="yes">Existential (∃_e)</property>
+                                            <property name="response_id">0</property>
+                                          </widget>
+                                          <packing>
+                                            <property name="position">7</property>
+                                          </packing>
+                                        </child>
                                       </widget>
                                     </child>
                                     <child>

diff --git a/helm/software/matita/matitaGui.ml b/helm/software/matita/matitaGui.ml
index db26ba20a55d7575e54f6b9932e5c0d71aa1404e..8bc226ed4a4bdbbbf33292d7afaa3a4f75c6f406 100644 (file)
--- a/helm/software/matita/matitaGui.ml
+++ b/helm/software/matita/matitaGui.ml
@@ -795,6 +795,16 @@ class gui () =
         (fun () -> source_buffer#insert "apply rule (lem …);\n");
       connect_button main#butDischarge
         (fun () -> source_buffer#insert "apply rule (discharge […]);\n");
+      
+      connect_button main#butForall_intro
+        (fun () -> source_buffer#insert "apply rule (∀_i {…} (…));\n");
+      connect_button main#butForall_elim
+        (fun () -> source_buffer#insert "apply rule (∀_e {…} (…));\n");
+      connect_button main#butExists_intro
+        (fun () -> source_buffer#insert "apply rule (∃_i {…} (…));\n");
+      connect_button main#butExists_elim
+        (fun () -> source_buffer#insert 
+          "apply rule (∃_e (…) {…} […] (…));\n\t[\n\t|\n\t]\n");
 
     
       (* TO BE REMOVED *)