Dummy dependent products in inductive types arities are no longer cleaned.

[helm.git] / helm / software / matita / library / technicalities / setoids.ma

diff --git a/helm/software/matita/library/technicalities/setoids.ma b/helm/software/matita/library/technicalities/setoids.ma
index 0f3bda302d116a7b8bfbf7a9a1736c9cfab70d23..4c51d3a448e15a900e8b28f2118cb480139614fd 100644 (file)
--- a/helm/software/matita/library/technicalities/setoids.ma
+++ b/helm/software/matita/library/technicalities/setoids.ma
@@ -18,8 +18,8 @@
 set "baseuri" "cic:/matita/technicalities/setoids".
 
 include "datatypes/constructors.ma".
-include "logic/connectives2.ma".
 include "logic/coimplication.ma".
+include "logic/connectives2.ma".
 
 (* DEFINITIONS OF Relation_Class AND n-ARY Morphism_Theory *)
 
@@ -150,14 +150,12 @@ definition morphism_theory_of_function :
     Morphism_Theory In' Out'.
   intros;
   apply (mk_Morphism_Theory ? ? f);
-  unfold In' in f; clear In';
-  unfold Out' in f; clear Out';
+  unfold In' in f ⊢ %; clear In';
+  unfold Out' in f ⊢ %; clear Out';
   generalize in match f; clear f;
   elim In;
    [ unfold make_compatibility_goal;
-     simplify;
-     intros;
-     whd;
+     whd; intros;
      reflexivity
    | simplify;
      intro;
@@ -205,13 +203,29 @@ definition equality_morphism_of_symmetric_areflexive_transitive_relation:
  apply mk_Morphism_Theory;
   [ exact Aeq
   | unfold make_compatibility_goal;
-    simplify;
+    simplify; unfold ASetoidClass; simplify;
     intros;
     split;
     unfold transitive in H;
     unfold symmetric in sym;
     intro;
-    auto new
+      [ apply (H x2 x1 x3 ? ?);
+          [apply (sym x1 x2 ?).
+           apply (H1).
+          |apply (H x1 x x3 ? ?);
+            [apply (H3).
+            |apply (H2).
+            ]
+          ]
+      | apply (H x1 x3 x ? ?);
+         [apply (H x1 x2 x3 ? ?);
+            [apply (H1).
+            |apply (H3).
+            ]
+         |apply (sym x x3 ?).
+          apply (H2).
+         ]
+      ]
   ].
 qed.
 
@@ -222,14 +236,33 @@ definition equality_morphism_of_symmetric_reflexive_transitive_relation:
     (Morphism_Theory (cons ? ASetoidClass (singl ? ASetoidClass)) Iff_Relation_Class).
  intros;
  apply mk_Morphism_Theory;
- reduce;
+ normalize;
   [ exact Aeq
   | intros;
     split;
     intro;
     unfold transitive in H;
     unfold symmetric in sym;
-    auto depth=4.
+    [ apply (H x2 x1 x3 ? ?);
+        [apply (sym x1 x2 ?).
+         apply (H1).
+        |apply (H x1 x x3 ? ?);
+          [apply (H3).
+          |apply (H2).
+          ]
+        ]
+    | apply (H x1 x2 x ? ?);
+      [apply (H1).
+      |apply (H x2 x3 x ? ?);
+        [apply (H3).
+        |apply (sym x x3 ?).
+         apply (H x x3 x3 ? ?);
+          [apply (H2).
+          |apply (refl x3).
+          ]
+        ]
+      ]
+    ]
   ]
 qed.
 
@@ -242,11 +275,17 @@ definition equality_morphism_of_asymmetric_areflexive_transitive_relation:
  apply mk_Morphism_Theory;
  [ simplify;
    apply Aeq
- | simplify;
+ | simplify; unfold ASetoidClass1; simplify; unfold ASetoidClass2; simplify;
    intros;
    whd;
    intros;
-   auto
+   apply (H x2 x1 x3 ? ?);
+    [apply (H1).
+    |apply (H x1 x x3 ? ?);
+      [apply (H3).
+      |apply (H2).
+      ]
+    ]
  ].
 qed.
 
@@ -259,11 +298,17 @@ definition equality_morphism_of_asymmetric_reflexive_transitive_relation:
  apply mk_Morphism_Theory;
  [ simplify;
    apply Aeq
- | simplify;
+ | simplify; unfold ASetoidClass1; simplify; unfold ASetoidClass2; simplify;
    intros;
    whd;
    intro;
-   auto
+   apply (H x2 x1 x3 ? ?);
+     [apply (H1).
+     |apply (H x1 x x3 ? ?);
+       [apply (H3).
+       |apply (H2).
+       ]
+     ]
  ].
 qed.
 
@@ -287,7 +332,7 @@ definition morphism_theory_of_predicate :
   | generalize in match f; clear f;
     unfold In'; clear In';
     elim In;
-     [ reduce;
+     [ normalize;
        intro;
        apply iff_refl
      | simplify;
@@ -303,7 +348,8 @@ theorem impl_trans: transitive ? impl.
  whd;
  unfold impl;
  intros;
- auto.
+ apply (H1 ?).apply (H ?).apply (H2).
+ autobatch.
 qed.
 
 (*DA PORTARE: Add Relation Prop impl
@@ -612,26 +658,21 @@ theorem apply_morphism_compatibility_Right2Left:
      generalize in match args1; clear args1;
      generalize in match m2; clear m2;
      generalize in match m1; clear m1;
-     elim t 0;
+     elim t 0; simplify;
       [ intros (T1 r Hs Hr m1 m2 args1 args2 H H1);
-        simplify in H;
-        simplify in H1;
-        simplify;
         apply H;
         exact H1
       | intros 8 (v T1 r Hr m1 m2 args1 args2);
-        cases v;
+        cases v; 
+        simplify;
         intros (H H1);
-        simplify in H1;
-        apply H;
-        exact H1
+        apply (H ? ? H1);
       | intros;
         apply H1;
         exact H2
       | intros 7 (v);
-        cases v;
+        cases v; simplify;
         intros (H H1);
-        simplify in H1;
         apply H;
         exact H1
       | intros;
@@ -653,9 +694,10 @@ theorem apply_morphism_compatibility_Right2Left:
      generalize in match H2; clear H2;
      elim args2 0; clear args2;
      elim args1; clear args1;
+     simplify in H2;
+     change in H2:(? ? %) with 
+       (relation_of_product_of_arguments Right2Left n t2 t4);
      elim H2; clear H2;
-     change in H4 with
-      (relation_of_product_of_arguments Right2Left n t2 t4);
      change with
       (relation_of_relation_class unit Out (apply_morphism n Out (m1 t3) t4)
         (apply_morphism n Out (m2 t1) t2));
@@ -726,10 +768,9 @@ theorem apply_morphism_compatibility_Left2Right:
         directed_relation_of_relation_class Left2Right ?
          (apply_morphism ? ? m1 args1)
          (apply_morphism ? ? m2 args2).
-  intro;
-  elim In;
-   [ simplify in m1 m2 args1 args2 ⊢ %;
-     change in H1 with
+  intro; 
+  elim In 0; simplify; intros;
+   [ change in H1 with
       (directed_relation_of_argument_class
         (get_rewrite_direction Left2Right t) t args1 args2);
      generalize in match H1; clear H1;
@@ -738,11 +779,8 @@ theorem apply_morphism_compatibility_Left2Right:
      generalize in match args1; clear args1;
      generalize in match m2; clear m2;
      generalize in match m1; clear m1;
-     elim t 0;
+     elim t 0; simplify;
       [ intros (T1 r Hs Hr m1 m2 args1 args2 H H1);
-        simplify in H;
-        simplify in H1;
-        simplify;
         apply H;
         exact H1
       | intros 8 (v T1 r Hr m1 m2 args1 args2);
@@ -779,9 +817,9 @@ theorem apply_morphism_compatibility_Left2Right:
      generalize in match H2; clear H2;
      elim args2 0; clear args2;
      elim args1; clear args1;
+     simplify in H2; change in H2:(? ? %) with
+       (relation_of_product_of_arguments Left2Right n t2 t4); 
      elim H2; clear H2;
-     change in H4 with
-      (relation_of_product_of_arguments Left2Right n t2 t4);
      change with
       (relation_of_relation_class unit Out (apply_morphism n Out (m1 t1) t2)
         (apply_morphism n Out (m2 t3) t4));
@@ -793,7 +831,6 @@ theorem apply_morphism_compatibility_Left2Right:
      generalize in match m1; clear m1;
      elim t 0;
       [ intros (T1 r Hs Hr m1 m2 H1 t1 t3 H3);
-        simplify in H3;
         change in H1 with
          (∀x1,x2:T1.r x1 x2 → make_compatibility_goal_aux n Out (m1 x1) (m2 x2));
      | intro v;
@@ -862,7 +899,7 @@ definition interp :
      rewrite <
        (about_carrier_of_relation_class_and_relation_class_of_argument_class S);
      exact c1
-   | split;
+   | simplify;split;
       [ rewrite <
          (about_carrier_of_relation_class_and_relation_class_of_argument_class S);
         exact c1
@@ -893,7 +930,7 @@ definition interp_relation_class_list :
      rewrite <
        (about_carrier_of_relation_class_and_relation_class_of_argument_class S);
      exact c1
-  | split;
+  | simplify; split;
      [ rewrite <
         (about_carrier_of_relation_class_and_relation_class_of_argument_class S);
        exact c1
@@ -982,39 +1019,39 @@ Qed.
 (* impl IS A MORPHISM *)
 
 Add Morphism impl with signature iff ==> iff ==> iff as Impl_Morphism.
-unfold impl; tauto.
+unfold impl; tautobatch.
 Qed.
 
 (* and IS A MORPHISM *)
 
 Add Morphism and with signature iff ==> iff ==> iff as And_Morphism.
- tauto.
+ tautobatch.
 Qed.
 
 (* or IS A MORPHISM *)
 
 Add Morphism or with signature iff ==> iff ==> iff as Or_Morphism.
- tauto.
+ tautobatch.
 Qed.
 
 (* not IS A MORPHISM *)
 
 Add Morphism not with signature iff ==> iff as Not_Morphism.
- tauto.
+ tautobatch.
 Qed.
 
 (* THE SAME EXAMPLES ON impl *)
 
 Add Morphism and with signature impl ++> impl ++> impl as And_Morphism2.
- unfold impl; tauto.
+ unfold impl; tautobatch.
 Qed.
 
 Add Morphism or with signature impl ++> impl ++> impl as Or_Morphism2.
- unfold impl; tauto.
+ unfold impl; tautobatch.
 Qed.
 
 Add Morphism not with signature impl -→ impl as Not_Morphism2.
- unfold impl; tauto.
+ unfold impl; tautobatch.
 Qed.
 
 *)