Great: some significant progress in fixing universe levels.

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index 67db8176c9673a08ebd57e10f4266414df8063cf..3a7614fca8b652e8668375d3bc1024bc6b3166a4 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -12,36 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "logic/cprop_connectives.ma".
-
-definition Type0 := Type.
-definition Type1 := Type.
-definition Type2 := Type.
-definition Type3 := Type.
-definition Type0_lt_Type1 := (Type0 : Type1).
-definition Type1_lt_Type2 := (Type1 : Type2).
-definition Type2_lt_Type3 := (Type2 : Type3).
-
-definition Type_OF_Type0: Type0 → Type := λx.x.
-definition Type_OF_Type1: Type1 → Type := λx.x.
-definition Type_OF_Type2: Type2 → Type := λx.x.
-definition Type_OF_Type3: Type3 → Type := λx.x.
-coercion Type_OF_Type0.
-coercion Type_OF_Type1.
-coercion Type_OF_Type2.
-coercion Type_OF_Type3.
-
-definition CProp0 := Type0.
-definition CProp1 := Type1.
-definition CProp2 := Type2.
-(*
-definition CProp0_lt_CProp1 := (CProp0 : CProp1).
-definition CProp1_lt_CProp2 := (CProp1 : CProp2).
-
-definition CProp_OF_CProp0: CProp0 → CProp := λx.x.
-definition CProp_OF_CProp1: CProp1 → CProp := λx.x.
-definition CProp_OF_CProp2: CProp2 → CProp := λx.x.
-*)
+include "cprop_connectives.ma".
 
 record equivalence_relation (A:Type0) : Type1 ≝
  { eq_rel:2> A → A → CProp0;
@@ -194,8 +165,8 @@ definition CPROP: setoid1.
   | constructor 1;
      [ apply Iff
      | intros 1; split; intro; assumption
-     | intros 3; cases H; split; assumption
-     | intros 5; cases H; cases H1; split; intro;
+     | intros 3; cases i; split; assumption
+     | intros 5; cases i; cases i1; split; intro;
         [ apply (f2 (f x1)) | apply (f1 (f3 z1))]]]
 qed.
 
@@ -210,10 +181,10 @@ interpretation "if" 'if r = (if' __ r).
 definition and_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
   [ apply And
-  | intros; split; intro; cases H; split;
-     [ apply (if ?? e a1)
+  | intros; split; intro; cases a1; split;
+     [ apply (if ?? e a2)
      | apply (if ?? e1 b1)
-     | apply (fi ?? e a1)
+     | apply (fi ?? e a2)
      | apply (fi ?? e1 b1)]]
 qed.
 
@@ -222,7 +193,7 @@ interpretation "and_morphism" 'and a b = (fun21 ___ and_morphism a b).
 definition or_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
   [ apply Or
-  | intros; split; intro; cases H; [1,3:left |2,4: right]
+  | intros; split; intro; cases o; [1,3:left |2,4: right]
      [ apply (if ?? e a1)
      | apply (fi ?? e a1)
      | apply (if ?? e1 b1)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/depends b/helm/software/matita/contribs/formal_topology/overlap/depends
index 54bda9a40994b623087ac3fe1d47c365bbf9e2c4..4875f5928428cfb279e5e821a0487325b632f229 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/depends
+++ b/helm/software/matita/contribs/formal_topology/overlap/depends
@@ -2,10 +2,11 @@ o-basic_pairs.ma o-algebra.ma
 o-concrete_spaces.ma o-basic_pairs.ma o-saturations.ma
 o-saturations.ma o-algebra.ma
 basic_pairs.ma o-basic_pairs.ma relations.ma
-o-algebra.ma categories.ma logic/cprop_connectives.ma
+o-algebra.ma categories.ma
 o-formal_topologies.ma o-basic_topologies.ma
-categories.ma logic/cprop_connectives.ma
+categories.ma cprop_connectives.ma
 subsets.ma categories.ma o-algebra.ma
 relations.ma o-algebra.ma subsets.ma
 o-basic_topologies.ma o-algebra.ma o-saturations.ma
-logic/cprop_connectives.ma 
+cprop_connectives.ma logic/connectives.ma
+logic/connectives.ma 

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
index 55d692190fdae75667e0efdcb678d83e087b84c3..6be19d92c31ac4518d402650c362e85dc4b3fd9b 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "categories.ma".
-include "logic/cprop_connectives.ma". 
 
 inductive bool : Type0 := true : bool | false : bool.
 
@@ -76,7 +75,7 @@ record OAlgebra : Type2 := {
   (* ⇔ deve essere =, l'esiste debole *)
   oa_join_split:
       ∀I:SET.∀p.∀q:arrows2 SET1 I oa_P.
-       oa_overlap p (oa_join I q) ⇔ ∃i:I.oa_overlap p (q i);
+       oa_overlap p (oa_join I q) ⇔ ∃i:carr I.oa_overlap p (q i);
   (*oa_base : setoid;
   1) enum non e' il nome giusto perche' non e' suriettiva
   2) manca (vedere altro capitolo) la "suriettivita'" come immagine di insiemi di oa_base
@@ -186,14 +185,14 @@ constructor 1;
 | constructor 1;
    (* tenere solo una uguaglianza e usare la proposizione 9.9 per
       le altre (unicita' degli aggiunti e del simmetrico) *)
-   [ apply (λp,q. And4 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
+   [ apply (λp,q. And42 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
              (eq2 ? (or_f_minus_ ?? p) (or_f_minus_ ?? q)) 
              (eq2 ? (or_f_ ?? p) (or_f_ ?? q)) 
              (eq2 ? (or_f_star_ ?? p) (or_f_star_ ?? q))); 
    | whd; simplify; intros; repeat split; intros; apply refl2;
-   | whd; simplify; intros; cases H; clear H; split; 
+   | whd; simplify; intros; cases a; clear a; split; 
      intro a; apply sym1; generalize in match a;assumption;
-   | whd; simplify; intros; cases H; cases H1; clear H H1; split; intro a;
+   | whd; simplify; intros; cases a; cases a1; clear a a1; split; intro a;
      [ apply (.= (e a)); apply e4;
      | apply (.= (e1 a)); apply e5;
      | apply (.= (e2 a)); apply e6;

diff --git a/helm/software/matita/contribs/formal_topology/overlap/relations.ma b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
index f5141a2ed3bf34098ca92ea27126b90d515c2d95..e6f816156fe684296548c452f1d03a5583f2cd47 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -29,10 +29,10 @@ definition binary_relation_setoid: SET → SET → SET1.
      [ apply (λA,B.λr,r': binary_relation A B. ∀x,y. r x y ↔ r' x y)
      | simplify; intros 3; split; intro; assumption
      | simplify; intros 5; split; intro;
-       [ apply (fi ?? (H ??)) | apply (if ?? (H ??))] assumption
+       [ apply (fi ?? (f ??)) | apply (if ?? (f ??))] assumption
      | simplify;  intros 7; split; intro;
-        [ apply (if ?? (H1 ??)) | apply (fi ?? (H ??)) ]
-        [ apply (if ?? (H ??)) | apply (fi ?? (H1 ??)) ]
+        [ apply (if ?? (f1 ??)) | apply (fi ?? (f ??)) ]
+        [ apply (if ?? (f ??)) | apply (fi ?? (f1 ??)) ]
        assumption]]
 qed.
 
@@ -48,7 +48,7 @@ definition composition:
        (* carr to avoid universe inconsistency *)  
        apply (λs1:carr A.λs3:carr C.∃s2:carr B. s1 ♮R12 s2 ∧ s2 ♮R23 s3);
      | intros;
-       split; intro; cases H (w H3); clear H; exists; [1,3: apply w ]
+       split; intro; cases e2 (w H3); clear e2; exists; [1,3: apply w ]
         [ apply (. (e‡#)‡(#‡e1)); assumption
         | apply (. ((e \sup -1)‡#)‡(#‡(e1 \sup -1))); assumption]]
   | intros 8; split; intro H2; simplify in H2 ⊢ %;
@@ -87,7 +87,7 @@ definition REL: category1.
     split; assumption
   |6,7: intros 5; unfold composition; simplify; split; intro;
         unfold setoid1_of_setoid in x y; simplify in x y;
-        [1,3: cases H (w H1); clear H; cases H1; clear H1; unfold;
+        [1,3: cases e (w H1); clear e; cases H1; clear H1; unfold;
           [ apply (. (e ^ -1 : eq1 ? w x)‡#); assumption
           | apply (. #‡(e : eq1 ? w y)); assumption]
         |2,4: exists; try assumption; split;
@@ -210,7 +210,7 @@ definition minus_star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \s
     apply f; [ apply (if ?? (e ^ -1 ??)); | apply (if ?? (e ??)) ] assumption]
 qed.
 
-(* the same as * for a basic pair *)
+(* the same as Rest for a basic pair *)
 definition star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V) (Ω \sup U).
  intros; constructor 1;
   [ apply (λr: arrows1 ? U V.λS: Ω \sup V. {x | ∀y:carr V. x ♮r y → y ∈ S});
@@ -221,7 +221,7 @@ definition star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V)
     apply f; [ apply (if ?? (e ^ -1 ??)); | apply (if ?? (e ??)) ] assumption]
 qed.
 
-(* the same as - for a basic pair *)
+(* the same as Ext for a basic pair *)
 definition minus_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V) (Ω \sup U).
  intros; constructor 1;
   [ apply (λr: arrows1 ? U V.λS: Ω \sup V. {x | (*∃x:U. x ♮r y ∧ x ∈ S*)
@@ -294,11 +294,11 @@ qed.
 *)
 
 include "o-algebra.ma".
-
+axiom daemon: False.
 definition orelation_of_relation: ∀o1,o2:REL. arrows1 ? o1 o2 → ORelation (SUBSETS o1) (SUBSETS o2).
  intros;
  constructor 1;
-  [ constructor 1;
+  [ constructor 1; 
      [ apply (λU.image ?? t U);
      | intros; apply (#‡e); ]
   | constructor 1;

diff --git a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
index 73872bfed5f8bceeb5605d28fd614abb6fe83cc9..6351fead91eca85d504ca36b96a93d70a4153db2 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
@@ -203,7 +203,7 @@ definition SUBSETS: objs1 SET → OAlgebra.
        (* senza questa change, universe inconsistency *)
        change in ⊢ (? ? (λ_:%.?)) with (carr I);
        exists [apply w1] exists [apply w] assumption;
-     | cases H; cases x; exists; [apply w1]
+     | cases e; cases x; exists; [apply w1]
         [ assumption
         | (* senza questa change, universe inconsistency *)
           whd; change in ⊢ (? ? (λ_:%.?)) with (carr I);