X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fo-basic_topologies.ma;h=8847eef3157fbdf9c8ec2969894997ea49b4b493;hb=6b71ae123d3e412d43872b8b7965b7013a970d05;hp=ae695f624f92907864505483ad0f783db7641420;hpb=cdc1636c7b536f1e667a2418140b82be6f4e0e30;p=helm.git
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..8847eef31 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
@@ -1,4 +1,4 @@
-(**************************************************************************)
+ (**************************************************************************)
(* ___ *)
(* ||M|| *)
(* ||A|| A project by Andrea Asperti *)
@@ -19,16 +19,11 @@ record basic_topology: Type2 â
{ carrbt:> OA;
A: carrbt â carrbt;
J: carrbt â carrbt;
- A_is_saturation: is_saturation ? A;
- J_is_reduction: is_reduction ? J;
+ A_is_saturation: is_o_saturation ? A;
+ J_is_reduction: is_o_reduction ? J;
compatibility: âU,V. (A U >< J V) = (U >< J V)
}.
-lemma hint: OA â objs2 OA.
- intro; apply t;
-qed.
-coercion hint.
-
record continuous_relation (S,T: basic_topology) : Type2 â
{ cont_rel:> arrows2 OA S T;
(* reduces uses eq1, saturated uses eq!!! *)
@@ -40,24 +35,17 @@ definition continuous_relation_setoid: basic_topology â basic_topology â set
intros (S T); constructor 1;
[ apply (continuous_relation S T)
| constructor 1;
- [ (*apply (λr,s:continuous_relation S T.âb. eq1 (oa_P (carrbt S)) (A ? (râ» b)) (A ? (sâ» b)));*)
- apply (λr,s:continuous_relation S T.râ»* â (A S) = sâ»* â (A ?));
+ [ alias symbol "eq" = "setoid2 eq".
+ alias symbol "compose" = "category2 composition".
+ apply (λr,s:continuous_relation S T. (râ»* ) â (A S) = (sâ»* â (A ?)));
| simplify; intros; apply refl2;
| simplify; intros; apply sym2; apply e
| simplify; intros; apply trans2; [2: apply e |3: apply e1; |1: skip]]]
qed.
-definition cont_rel': âS,T: basic_topology. continuous_relation_setoid S T â arrows2 ? S T â cont_rel.
-
-coercion cont_rel'.
-
-definition cont_rel'':
- âS,T: basic_topology.
- carr2 (continuous_relation_setoid S T) â ORelation_setoid (carrbt S) (carrbt T).
- intros; apply rule cont_rel; apply c;
-qed.
-
-coercion cont_rel''.
+definition continuous_relation_of_continuous_relation_setoid:
+ âP,Q. continuous_relation_setoid P Q â continuous_relation P Q â λP,Q,c.c.
+coercion continuous_relation_of_continuous_relation_setoid.
(*
theorem continuous_relation_eq':
@@ -108,7 +96,6 @@ theorem continuous_relation_eq_inv':
qed.
*)
-axiom daemon: False.
definition continuous_relation_comp:
âo1,o2,o3.
continuous_relation_setoid o1 o2 â
@@ -117,13 +104,10 @@ definition continuous_relation_comp:
intros (o1 o2 o3 r s); constructor 1;
[ apply (s â r);
| intros;
- apply sym1;
+ apply sym1;
change in match ((s â r) U) with (s (r U));
- (**) unfold FunClass_1_OF_Type_OF_setoid2;
- unfold objs2_OF_basic_topology1; unfold hint;
- letin reduced := reduced; clearbody reduced;
- unfold uncurry_arrows in reduced ⢠%; (**)
- apply (.= (reduced : ?)\sup -1);
+ (**) unfold FunClass_1_OF_carr2;
+ apply (.= (reduced : ?)\sup -1);
[ (*BAD*) change with (eq1 ? (r U) (J ? (r U)));
(* BAD U *) apply (.= (reduced ??? U ?)); [ assumption | apply refl1 ]
| apply refl1]
@@ -151,20 +135,15 @@ definition BTop: category2.
change in e with (aâ»* â A o1 = a'â»* â A o1);
change in e1 with (bâ»* â A o2 = b'â»* â A o2);
apply (.= eâ¡#);
- intro x;
- change with (bâ»* (a'â»* (A o1 x)) = b'â»*(a'â»* (A o1 x)));
- alias symbol "trans" = "trans1".
- alias symbol "prop1" = "prop11".
- alias symbol "invert" = "setoid1 symmetry".
- lapply (.= â (saturated o1 o2 a' (A o1 x) : ?));
- [3: apply (bâ»* ); | 5: apply Hletin; |1,2: skip;
- |apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1); ]
- change in e1 with (âx.bâ»* (A o2 x) = b'â»* (A o2 x));
+ intro x;
+ change with (eq1 ? (bâ»* (a'â»* (A o1 x))) (b'â»*(a'â»* (A o1 x))));
+ apply (.= â (saturated o1 o2 a' (A o1 x) ?)); [
+ apply ((o_saturation_idempotent ?? (A_is_saturation o1) x)^-1);]
apply (.= (e1 (a'â»* (A o1 x))));
- alias symbol "invert" = "setoid1 symmetry".
- lapply (â ((saturated ?? a' (A o1 x) : ?) ^ -1));
- [2: apply (b'â»* ); |4: apply Hletin; | skip;
- |apply ((saturation_idempotent ?? (A_is_saturation o1) x)^-1);]]
+ change with (eq1 ? (b'â»* (A o2 (a'â»* (A o1 x)))) (b'â»*(a'â»* (A o1 x))));
+ apply (.= â (saturated o1 o2 a' (A o1 x):?)^-1); [
+ apply ((o_saturation_idempotent ?? (A_is_saturation o1) x)^-1);]
+ apply rule #;]
| intros; simplify;
change with (((a34â»* â a23â»* ) â a12â»* ) â A o1 = ((a34â»* â (a23â»* â a12â»* )) â A o1));
apply rule (#â¡ASSOC ^ -1);
@@ -176,8 +155,12 @@ definition BTop: category2.
apply (#â¡(id_neutral_left2 : ?));]
qed.
-definition btop_carr: BTop â Type1 â λo:BTop. carr1 (oa_P (carrbt o)).
-coercion btop_carr.
+definition basic_topology_of_BTop: objs2 BTop â basic_topology â λx.x.
+coercion basic_topology_of_BTop.
+
+definition continuous_relation_setoid_of_arrows2_BTop :
+ âP,Q. arrows2 BTop P Q â continuous_relation_setoid P Q â λP,Q,x.x.
+coercion continuous_relation_setoid_of_arrows2_BTop.
(*
(*CSC: unused! *)