From: Enrico Tassi Date: Sun, 21 Dec 2008 21:58:47 +0000 (+0000) Subject: merged commits, the same proof is missing :-( X-Git-Tag: make_still_working~4339 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=6d14064e2494072f6c60c984a8c4419f07cdf723;p=helm.git merged commits, the same proof is missing :-( --- 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 9e8b473b6..12b348cc3 100644 --- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma +++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma @@ -17,11 +17,7 @@ include "logic/cprop_connectives.ma". inductive bool : Type := true : bool | false : bool. -<<<<<<< .mine -lemma BOOL : setoid. -======= lemma BOOL : objs1 SET. ->>>>>>> .r9407 constructor 1; [apply bool] constructor 1; [ intros (x y); apply (match x with [ true ⇒ match y with [ true ⇒ True | _ ⇒ False] | false ⇒ match y with [ true ⇒ False | false ⇒ True ]]); | whd; simplify; intros; cases x; apply I; @@ -42,17 +38,8 @@ lemma IF_THEN_ELSE_p : intros; cases x in H; cases y; simplify; intros; try apply refl; whd in H; cases H; qed. -<<<<<<< .mine -interpretation "unary morphism comprehension with no proof" 'comprehension T P = -======= -lemma if_then_else : ∀T:SET. ∀a,b:T. arrows1 SET BOOL T. -intros; constructor 1; intros; -[ apply (match c with [ true ⇒ t | false ⇒ t1 ]); -| apply (IF_THEN_ELSE_p T t t1 a a' H);] -qed. -interpretation "mk " 'comprehension T P = ->>>>>>> .r9407 +interpretation "unary morphism comprehension with no proof" 'comprehension T P = (mk_unary_morphism T _ P _). notation > "hvbox({ ident i ∈ s | term 19 p | by })" with precedence 90 @@ -63,24 +50,13 @@ for @{ 'comprehension_by $s (λ${ident i}:$_. $p) $by}. interpretation "unary morphism comprehension with proof" 'comprehension_by s \eta.f p = (mk_unary_morphism s _ f p). -<<<<<<< .mine -======= -definition A : ∀S:SET.∀a,b:S.arrows1 SET BOOL S. -apply (λS,a,b.{ x ∈ BOOL | match x with [ true ⇒ a | false ⇒ b] | IF_THEN_ELSE_p S a b}). -qed. ->>>>>>> .r9407 record OAlgebra : Type := { oa_P :> SET; oa_leq : binary_morphism1 oa_P oa_P CPROP; (* CPROP is setoid1 *) oa_overlap: binary_morphism1 oa_P oa_P CPROP; -<<<<<<< .mine - oa_meet: ∀I:setoid.unary_morphism (unary_morphism_setoid I oa_P) oa_P; - oa_join: ∀I:setoid.unary_morphism (unary_morphism_setoid I oa_P) oa_P; -======= oa_meet: ∀I:SET.unary_morphism (arrows1 SET I oa_P) oa_P; oa_join: ∀I:SET.unary_morphism (arrows1 SET I oa_P) oa_P; ->>>>>>> .r9407 oa_one: oa_P; oa_zero: oa_P; oa_leq_refl: ∀a:oa_P. oa_leq a a; @@ -94,17 +70,10 @@ record OAlgebra : Type := { oa_overlap_preservers_meet: ∀p,q.oa_overlap p q → oa_overlap p (oa_meet ? { x ∈ BOOL | match x with [ true ⇒ p | false ⇒ q ] | IF_THEN_ELSE_p oa_P p q }); -<<<<<<< .mine - oa_join_split: - ∀I:setoid.∀p.∀q:I ⇒ oa_P.oa_overlap p (oa_join I q) ⇔ ∃i:I.oa_overlap p (q i); - (* - oa_base : setoid; -======= (*(oa_meet BOOL (if_then_else oa_P p q));*) oa_join_split: (* ha I → oa_P da castare a funX (ums A oa_P) *) ∀I:SET.∀p.∀q:arrows1 SET I oa_P.oa_overlap p (oa_join I q) ⇔ ∃i:I.oa_overlap p (q i); (*oa_base : setoid; ->>>>>>> .r9407 oa_enum : ums oa_base oa_P; oa_density: ∀p,q.(∀i.oa_overlap p (oa_enum i) → oa_overlap q (oa_enum i)) → oa_leq p q *) @@ -181,16 +150,8 @@ intros (P Q); constructor 1; [ apply (ORelation P Q); | constructor 1; -<<<<<<< .mine - [ alias symbol "and" = "constructive and". - apply (λp,q. And4 (∀a.p⎻* a = q⎻* a) (∀a.p⎻ a = q⎻ a) - (∀a.p a = q a) (∀a.p* a = q* a)); - | whd; simplify; intros; repeat split; intros; apply refl; -======= - [ apply (λp,q. eq1 ? p⎻* q⎻* ∧ eq1 ? p⎻ q⎻ ∧ eq1 ? p q ∧ eq1 ? p* q* ); + [ apply (λp,q. And4 (eq1 ? p⎻* q⎻* ) (eq1 ? p⎻ q⎻) (eq1 ? p q) (eq1 ? p* q* )); | whd; simplify; intros; repeat split; intros; apply refl1; ->>>>>>> .r9407 -<<<<<<< .mine | whd; simplify; intros; cases H; clear H; split; intro a; apply sym; generalize in match a;assumption; | whd; simplify; intros; cases H; cases H1; clear H H1; split; intro a; @@ -199,24 +160,7 @@ constructor 1; | apply (.= (H4 a)); apply H8; | apply (.= (H5 a)); apply H9;]]] qed. -======= - | whd; simplify; intros; cases H; cases H1; cases H3; clear H H3 H1; - repeat split; intros; apply sym1; assumption; - | whd; simplify; intros; cases H; cases H1; cases H2; cases H4; cases H6; cases H8; - repeat split; intros; clear H H1 H2 H4 H6 H8; apply trans1; - [2: apply H10; - |5: apply H11; - |8: apply H7; - |11: apply H3; - |1,4,7,10: skip - |*: assumption - ]]] -qed. ->>>>>>> .r9407 -<<<<<<< .mine -definition ORelation_composition : ∀P,Q,R. -======= lemma hint1 : ∀P,Q. ORelation_setoid P Q → arrows1 SET P Q. intros; apply (or_f ?? c);qed. coercion hint1. @@ -226,35 +170,12 @@ coercion hint3. lemma hint2: OAlgebra → setoid. intros; apply (oa_P o). qed. coercion hint2. -definition composition : ∀P,Q,R. ->>>>>>> .r9407 +definition ORelation_composition : ∀P,Q,R. binary_morphism1 (ORelation_setoid P Q) (ORelation_setoid Q R) (ORelation_setoid P R). intros; constructor 1; [ intros (F G); constructor 1; -<<<<<<< .mine - [ apply {x ∈ P | G (F x)}; intros; simplify; apply (†(†H)); - | apply {x ∈ P | G⎻* (F⎻* x)}; intros; simplify; apply (†(†H)); - | apply {x ∈ R | F* (G* x)}; intros; simplify; apply (†(†H)); - | apply {x ∈ R | F⎻ (G⎻ x)}; intros; simplify; apply (†(†H)); - | intros; simplify; - lapply (or_prop1 ?? G (F p) q) as H1; lapply (or_prop1 ?? F p (G* q)) as H2; - split; intro H; - [ apply (if1 ?? H2); apply (if1 ?? H1); apply H; - | apply (fi1 ?? H1); apply (fi1 ?? H2); apply H;] - | intros; simplify; - lapply (or_prop2 ?? G p (F⎻* q)) as H1; lapply (or_prop2 ?? F (G⎻ p) q) as H2; - split; intro H; - [ apply (if1 ?? H1); apply (if1 ?? H2); apply H; - | apply (fi1 ?? H2); apply (fi1 ?? H1); apply H;] - | intros; simplify; - lapply (or_prop3 ?? F p (G⎻ q)) as H1; lapply (or_prop3 ?? G (F p) q) as H2; - split; intro H; - [ apply (if1 ?? H1); apply (if1 ?? H2); apply H; - | apply (fi1 ?? H2); apply (fi1 ?? H1); apply H;]] -| intros; simplify; split; simplify; intros; elim DAEMON;] -======= [ apply (G ∘ F); | apply (G⎻* ∘ F⎻* ); | apply (F* ∘ G* ); @@ -279,7 +200,6 @@ constructor 1; lapply (.= ((†H1)‡#)); [8: apply Hletin; [ apply trans1; [2: lapply (prop1); [apply Hletin; *)] ->>>>>>> .r9407 qed. definition OA : category1. @@ -287,21 +207,11 @@ split; [ apply (OAlgebra); | intros; apply (ORelation_setoid o o1); | intro O; split; -<<<<<<< .mine - [1,2,3,4: constructor 1; [1,3,5,7:apply (λx.x);|*:intros;assumption] - |5,6,7:intros;split;intros; assumption;] -|4: apply ORelation_composition; -|*: elim DAEMON;] -qed. - - - -======= [1,2,3,4: apply id1; |5,6,7:intros; apply refl1;] -| apply composition; -| intros; repeat split; unfold composition; simplify; - [1,3: apply (comp_assoc1); | 2,4: apply ((comp_assoc1 ????????) \sup -1);] -| intros; repeat split; unfold composition; simplify; apply id_neutral_left1; -| intros; repeat split; unfold composition; simplify; apply id_neutral_right1;] -qed.>>>>>>> .r9407 +| apply ORelation_composition; +| intros; repeat split; unfold ORelation_composition; simplify; + [1,3: apply (comp_assoc1); | 2,4: apply ((comp_assoc1 :?) ^ -1);] +| intros; repeat split; unfold ORelation_composition; simplify; apply id_neutral_left1; +| intros; repeat split; unfold ORelation_composition; simplify; apply id_neutral_right1;] +qed.