X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fconcrete_spaces.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fconcrete_spaces.ma;h=0000000000000000000000000000000000000000;hb=1ed4fe0f28d3b0b915387330cd722bfb80fb1063;hp=791af46b3431b63992ab482889077ca5d0dfeb71;hpb=05cfeb82d2624860e66941421a937f308d66cf33;p=helm.git diff --git a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma deleted file mode 100644 index 791af46b3..000000000 --- a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma +++ /dev/null @@ -1,109 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_pairs.ma". - -(* carr1 e' necessario perche' ci sega via la coercion per gli oggetti di REL! - (confondendola con la coercion per gli oggetti di SET *) -record concrete_space : Type1 ≝ - { bp:> BP; - converges: ∀a: carr1 (concr bp).∀U,V: carr1 (form bp). a ⊩ U → a ⊩ V → a ⊩ (U ↓ V); - all_covered: ∀x: carr1 (concr bp). x ⊩ form bp - }. - -record convergent_relation_pair (CS1,CS2: concrete_space) : Type1 ≝ - { rp:> arrows1 ? CS1 CS2; - respects_converges: - ∀b,c. - minus_image ?? rp \sub\c (BPextS CS2 (b ↓ c)) = - BPextS CS1 ((minus_image ?? rp \sub\f b) ↓ (minus_image ?? rp \sub\f c)); - respects_all_covered: - minus_image ?? rp\sub\c (BPextS CS2 (full_subset (form CS2))) = BPextS CS1 (full_subset (form CS1)) - }. -(* -definition convergent_relation_space_setoid: concrete_space → concrete_space → setoid1. - intros; - constructor 1; - [ apply (convergent_relation_pair c c1) - | constructor 1; - [ intros; - apply (relation_pair_equality c c1 c2 c3); - | intros 1; apply refl1; - | intros 2; apply sym1; - | intros 3; apply trans1]] -qed. - -definition convergent_relation_space_composition: - ∀o1,o2,o3: concrete_space. - binary_morphism1 - (convergent_relation_space_setoid o1 o2) - (convergent_relation_space_setoid o2 o3) - (convergent_relation_space_setoid o1 o3). - intros; constructor 1; - [ intros; whd in c c1 ⊢ %; - constructor 1; - [ apply (fun1 ??? (comp1 BP ???)); [apply (bp o2) |*: apply rp; assumption] - | intros; - change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c); - change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? (? ? ? (? ? ? %) ?) ?))) - with (c1 \sub \f ∘ c \sub \f); - change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? ? (? ? ? (? ? ? %) ?)))) - with (c1 \sub \f ∘ c \sub \f); - apply (.= (extS_com ??????)); - apply (.= (†(respects_converges ?????))); - apply (.= (respects_converges ?????)); - apply (.= (†(((extS_com ??????) \sup -1)‡(extS_com ??????)\sup -1))); - apply refl1; - | change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c); - apply (.= (extS_com ??????)); - apply (.= (†(respects_all_covered ???))); - apply (.= respects_all_covered ???); - apply refl1] - | intros; - change with (b ∘ a = b' ∘ a'); - change in H with (rp'' ?? a = rp'' ?? a'); - change in H1 with (rp'' ?? b = rp ?? b'); - apply (.= (H‡H1)); - apply refl1] -qed. - -definition CSPA: category1. - constructor 1; - [ apply concrete_space - | apply convergent_relation_space_setoid - | intro; constructor 1; - [ apply id1 - | intros; - unfold id; simplify; - apply (.= (equalset_extS_id_X_X ??)); - apply (.= (†((equalset_extS_id_X_X ??)\sup -1‡ - (equalset_extS_id_X_X ??)\sup -1))); - apply refl1; - | apply (.= (equalset_extS_id_X_X ??)); - apply refl1] - | apply convergent_relation_space_composition - | intros; simplify; - change with (a34 ∘ (a23 ∘ a12) = (a34 ∘ a23) ∘ a12); - apply (.= ASSOC1); - apply refl1 - | intros; simplify; - change with (a ∘ id1 ? o1 = a); - apply (.= id_neutral_right1 ????); - apply refl1 - | intros; simplify; - change with (id1 ? o2 ∘ a = a); - apply (.= id_neutral_left1 ????); - apply refl1] -qed. -*) \ No newline at end of file