From ac1263c3471b351f520d7e2abf217220efc10e7e Mon Sep 17 00:00:00 2001
From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Sun, 28 Dec 2008 16:52:37 +0000
Subject: [PATCH] Many universe inconsistency avoided here and there.

---
 .../formal_topology/overlap/subsets.ma        | 33 ++++++++++++-------
 1 file changed, 22 insertions(+), 11 deletions(-)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
index 4bbe7fdbe..9847d4c55 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
@@ -153,24 +153,26 @@ definition big_intersects:
      | apply (. (#‡(e i)\sup -1)); apply f]]
 qed.
 
-axiom (*definition*) big_union:
+(* senza questo exT "fresco", universe inconsistency *)
+inductive exT (A:Type) (P:A→CProp) : CProp ≝
+  ex_introT: ∀w:A. P w → exT A P.
+
+definition big_union:
  ∀A:SET.∀I:SET.unary_morphism2 (setoid1_of_setoid I ⇒ Ω \sup A) (setoid2_of_setoid1 (Ω \sup A)).
-(* intros; constructor 1;
+ intros; constructor 1;
   [ intro; whd; whd in A; whd in I;
-    apply ({x | ∃i:I. x ∈ t i});
+    apply ({x | (*∃i:carr I. x ∈ t i*) exT (carr I) (λi. x ∈ t i)});
     simplify; intros; split; intros; cases H; clear H; exists; [1,3:apply w]
     [ apply (. (e‡#)); | apply (. (e \sup -1‡#)); ]
     apply x;
   | intros; split; intros 2; simplify in f ⊢ %; cases f; clear f; exists; [1,3:apply w]
      [ apply (. (#‡(e w))); apply x;
      | apply (. (#‡(e w)\sup -1)); apply x]]
-qed.*)
+qed.
 
 (* incluso prima non funziona piu' nulla *)
 include "o-algebra.ma".
 
-
-axiom daemon: False.
 definition SUBSETS: objs1 SET → OAlgebra.
  intro A; constructor 1;
   [ apply (Ω \sup A);
@@ -187,18 +189,27 @@ definition SUBSETS: objs1 SET → OAlgebra.
   | intros; apply transitive_subseteq_operator; [2: apply f; | skip | assumption]
   | intros; cases f; exists [apply w] assumption
   | intros; intros 2; apply (f ? f1 i);
-  |(* intros; intros 2; apply f; exists; [apply i] assumption;*)
+  | intros; intros 2; apply f;
+    (* senza questa change, universe inconsistency *)
+    whd; change in ⊢ (? ? (λ_:%.?)) with (carr I);
+    exists; [apply i] assumption;
   | intros 3; cases f;
   | intros 3; constructor 1;
   | intros; cases f; exists; [apply w]
      [ assumption
      | whd; intros; cases i; simplify; assumption]
-  |(* intros; split; intro;
-     [ cases f; cases x1; exists [apply w1] exists [apply w] assumption;
-     | cases H; cases x; exists; [apply w1] [assumption | exists; [apply w] assumption]]*)
+  | intros; split; intro;
+     [ cases f; cases x1;
+       (* 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]
+        [ assumption
+        | (* senza questa change, universe inconsistency *)
+          whd; change in ⊢ (? ? (λ_:%.?)) with (carr I);
+          exists; [apply w] assumption]]
   | intros; intros 2; cases (H (singleton ? a) ?);
      [ exists; [apply a] [assumption | change with (a = a); apply refl1;]
      | change in x1 with (a = w); change with (mem A a q); apply (. (x1 \sup -1‡#));
        assumption]]
-cases daemon;
 qed.
\ No newline at end of file
-- 
2.39.2