From a99fe3ca5a39b4d9754b69863b5f9fb0f91ed286 Mon Sep 17 00:00:00 2001
From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Tue, 6 Jan 2009 01:31:21 +0000
Subject: [PATCH] No more daemons, no more exTs.

---
 .../formal_topology/overlap/o-basic_topologies.ma      |  1 -
 .../contribs/formal_topology/overlap/relations.ma      | 10 +++-------
 .../matita/contribs/formal_topology/overlap/subsets.ma |  6 +-----
 3 files changed, 4 insertions(+), 13 deletions(-)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma b/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
index ae695f624..1081f5bea 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-basic_topologies.ma
@@ -108,7 +108,6 @@ theorem continuous_relation_eq_inv':
 qed.
 *)
 
-axiom daemon: False.
 definition continuous_relation_comp:
  ∀o1,o2,o3.
   continuous_relation_setoid o1 o2 →
diff --git a/helm/software/matita/contribs/formal_topology/overlap/relations.ma b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
index e6f816156..eb60386fe 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -174,9 +174,6 @@ lemma extS_com: ∀o1,o2,o3,c1,c2,S. extS o1 o3 (c2 ∘ c1) S = extS o1 o2 c1 (e
     assumption]
 qed.
 *)
-(* senza questo exT "fresco", universe inconsistency *)
-inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
-  ex_introT: ∀w:A. P w → exT A P.
 
 lemma hint: ∀U. carr U → Type_OF_setoid1 ?(*(setoid1_of_SET U)*).
  [ apply setoid1_of_SET; apply U
@@ -187,8 +184,7 @@ coercion hint.
 (* the same as ⋄ for a basic pair *)
 definition image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) (Ω \sup V).
  intros; constructor 1;
-  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | (*∃x:U. x ♮r y ∧ x ∈ S*)
-      exT ? (λx:carr U.x ♮r y ∧ x ∈ S) });
+  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∃x:carr U. x ♮r y ∧ x ∈ S });
     intros; simplify; split; intro; cases e1; exists [1,3: apply w]
      [ apply (. (#‡e)‡#); assumption
      | apply (. (#‡e ^ -1)‡#); assumption]
@@ -294,7 +290,7 @@ 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;
@@ -331,4 +327,4 @@ definition orelation_of_relation: ∀o1,o2:REL. arrows1 ? o1 o2 → ORelation (S
      | cases x1; cases x2; clear x1 x2; exists; [apply w1]
         [ exists; [apply w] split; assumption;
         | assumption; ]]]
-qed. sistemare anche l'hint da un'altra parte e capire l'exT (doppio!)
\ No newline at end of file
+qed. (*sistemare anche l'hint da un'altra parte *)
diff --git a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
index 6351fead9..41e29a4fb 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
@@ -153,15 +153,11 @@ definition big_intersects:
      | apply (. (#‡(e i)\sup -1)); apply f]]
 qed.
 
-(* senza questo exT "fresco", universe inconsistency *)
-inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
-  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;
   [ intro; whd; whd in A; whd in I;
-    apply ({x | (*∃i:carr I. x ∈ t i*) exT (carr I) (λi. x ∈ t i)});
+    apply ({x | ∃i:carr I. x ∈ t i });
     simplify; intros; split; intros; cases e1; clear e1; exists; [1,3:apply w]
     [ apply (. (e‡#)); | apply (. (e \sup -1‡#)); ]
     apply x;
-- 
2.39.2