X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fo-algebra.ma;h=806859a45dd0ae4e3d70d265843b9a54bdeaf0a4;hb=c2123cdb49560cc6ef2a86b71ab21b432581c076;hp=b17dacbaf8a01ab107d8cd24914f9599899e511b;hpb=6b71ae123d3e412d43872b8b7965b7013a970d05;p=helm.git

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 b17dacbaf..806859a45 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
@@ -34,9 +34,9 @@ intros; cases x in e; cases y; simplify; intros; try apply refl1; whd in e; case
 qed.
 
 interpretation "unary morphism comprehension with no proof" 'comprehension T P = 
-  (mk_unary_morphism T _ P _).
+  (mk_unary_morphism T ? P ?).
 interpretation "unary morphism1 comprehension with no proof" 'comprehension T P = 
-  (mk_unary_morphism1 T _ P _).
+  (mk_unary_morphism1 T ? P ?).
 
 notation > "hvbox({ ident i ∈ s | term 19 p | by })" with precedence 90
 for @{ 'comprehension_by $s (λ${ident i}. $p) $by}.
@@ -44,9 +44,9 @@ notation < "hvbox({ ident i ∈ s | term 19 p })" with precedence 90
 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).
+  (mk_unary_morphism s ? f p).
 interpretation "unary morphism1 comprehension with proof" 'comprehension_by s \eta.f p = 
-  (mk_unary_morphism1 s _ f p).
+  (mk_unary_morphism1 s ? f p).
 
 (* per il set-indexing vedere capitolo BPTools (foundational tools), Sect. 0.3.4 complete
    lattices, Definizione 0.9 *)
@@ -65,8 +65,8 @@ record OAlgebra : Type2 := {
   oa_overlap_sym: ∀a,b:oa_P.oa_overlap a b → oa_overlap b a;
   oa_meet_inf: 
     ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.
-      oa_leq p (oa_meet I p_i) = ∀i:I.oa_leq p (p_i i);
-  oa_join_sup: ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.oa_leq (oa_join I p_i) p = ∀i:I.oa_leq (p_i i) p;
+      oa_leq p (oa_meet I p_i) = (∀i:I.oa_leq p (p_i i));
+  oa_join_sup: ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.oa_leq (oa_join I p_i) p = (∀i:I.oa_leq (p_i i) p);
   oa_zero_bot: ∀p:oa_P.oa_leq oa_zero p;
   oa_one_top: ∀p:oa_P.oa_leq p oa_one;
   oa_overlap_preserves_meet_: 
@@ -74,7 +74,7 @@ record OAlgebra : Type2 := {
        (oa_meet ? { x ∈ BOOL | match x with [ true ⇒ p | false ⇒ q ] | IF_THEN_ELSE_p oa_P p q });
   oa_join_split:
       ∀I:SET.∀p.∀q:I ⇒ oa_P.
-       oa_overlap p (oa_join I q) = ∃i:I.oa_overlap p (q i);
+       oa_overlap p (oa_join I q) = (∃i:I.oa_overlap p (q i));
   (*oa_base : setoid;
   1) enum non e' il nome giusto perche' non e' suriettiva
   2) manca (vedere altro capitolo) la "suriettivita'" come immagine di insiemi di oa_base
@@ -85,11 +85,11 @@ record OAlgebra : Type2 := {
       ∀p,q.(∀r.oa_overlap p r → oa_overlap q r) → oa_leq p q
 }.
 
-interpretation "o-algebra leq" 'leq a b = (fun21 ___ (oa_leq _) a b).
+interpretation "o-algebra leq" 'leq a b = (fun21 ??? (oa_leq ?) a b).
 
 notation "hovbox(a mpadded width -150% (>)< b)" non associative with precedence 45
 for @{ 'overlap $a $b}.
-interpretation "o-algebra overlap" 'overlap a b = (fun21 ___ (oa_overlap _) a b).
+interpretation "o-algebra overlap" 'overlap a b = (fun21 ??? (oa_overlap ?) a b).
 
 notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (∧) \below (\emsp) \nbsp term 90 p)" 
 non associative with precedence 50 for @{ 'oa_meet $p }.
@@ -99,9 +99,9 @@ non associative with precedence 50 for @{ 'oa_meet_mk (λ${ident i}:$I.$p) }.
 notation > "hovbox(∧ f)" non associative with precedence 60
 for @{ 'oa_meet $f }.
 interpretation "o-algebra meet" 'oa_meet f = 
-  (fun12 __ (oa_meet __) f).
+  (fun12 ?? (oa_meet ??) f).
 interpretation "o-algebra meet with explicit function" 'oa_meet_mk f = 
-  (fun12 __ (oa_meet __) (mk_unary_morphism _ _ f _)).
+  (fun12 ?? (oa_meet ??) (mk_unary_morphism ?? f ?)).
 
 notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (∨) \below (\emsp) \nbsp term 90 p)" 
 non associative with precedence 50 for @{ 'oa_join $p }.
@@ -111,9 +111,9 @@ non associative with precedence 50 for @{ 'oa_join_mk (λ${ident i}:$I.$p) }.
 notation > "hovbox(∨ f)" non associative with precedence 60
 for @{ 'oa_join $f }.
 interpretation "o-algebra join" 'oa_join f = 
-  (fun12 __ (oa_join __) f).
+  (fun12 ?? (oa_join ??) f).
 interpretation "o-algebra join with explicit function" 'oa_join_mk f = 
-  (fun12 __ (oa_join __) (mk_unary_morphism _ _ f _)).
+  (fun12 ?? (oa_join ??) (mk_unary_morphism ?? f ?)).
 
 definition binary_meet : ∀O:OAlgebra. binary_morphism1 O O O.
 intros; split;
@@ -127,7 +127,7 @@ intros; split;
 qed.
 
 interpretation "o-algebra binary meet" 'and a b = 
-  (fun21 ___ (binary_meet _) a b).
+  (fun21 ??? (binary_meet ?) a b).
 
 prefer coercion Type1_OF_OAlgebra.
 
@@ -143,7 +143,7 @@ intros; split;
 qed.
 
 interpretation "o-algebra binary join" 'or a b = 
-  (fun21 ___ (binary_join _) a b).
+  (fun21 ??? (binary_join ?) a b).
 
 lemma oa_overlap_preservers_meet: ∀O:OAlgebra.∀p,q:O.p >< q → p >< (p ∧ q).
 (* next change to avoid universe inconsistency *)
@@ -166,9 +166,9 @@ notation > "hovbox(a ∨ b)" left associative with precedence 49
 for @{ 'oa_join (mk_unary_morphism BOOL ? (λx__:bool.match x__ with [ true ⇒ $a | false ⇒ $b ]) (IF_THEN_ELSE_p ? $a $b)) }.
 
 interpretation "o-algebra join" 'oa_join f = 
-  (fun12 __ (oa_join __) f).
+  (fun12 ?? (oa_join ??) f).
 interpretation "o-algebra join with explicit function" 'oa_join_mk f = 
-  (fun12 __ (oa_join __) (mk_unary_morphism _ _ f _)).
+  (fun12 ?? (oa_join ??) (mk_unary_morphism ?? f ?)).
 
 record ORelation (P,Q : OAlgebra) : Type2 ≝ {
   or_f_ : carr2 (P ⇒ Q);
@@ -187,10 +187,11 @@ constructor 1;
 | constructor 1;
    (* tenere solo una uguaglianza e usare la proposizione 9.9 per
       le altre (unicita' degli aggiunti e del simmetrico) *)
-   [ apply (λp,q. And42 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
-             (eq2 ? (or_f_minus_ ?? p) (or_f_minus_ ?? q)) 
-             (eq2 ? (or_f_ ?? p) (or_f_ ?? q)) 
-             (eq2 ? (or_f_star_ ?? p) (or_f_star_ ?? q))); 
+   [ apply (λp,q. And42 
+             (or_f_minus_star_ ?? p = or_f_minus_star_ ?? q) 
+             (or_f_minus_ ?? p = or_f_minus_ ?? q) 
+             (or_f_ ?? p = or_f_ ?? q) 
+             (or_f_star_ ?? p = or_f_star_ ?? q)); 
    | whd; simplify; intros; repeat split; intros; apply refl2;
    | whd; simplify; intros; cases a; clear a; split; 
      intro a; apply sym1; generalize in match a;assumption;
@@ -244,9 +245,9 @@ notation > "r⎻*" non associative with precedence 90 for @{'OR_f_minus_star $r}
 notation "r \sup ⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
 notation > "r⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
 
-interpretation "o-relation f⎻*" 'OR_f_minus_star r = (fun12 __ (or_f_minus_star _ _) r).
-interpretation "o-relation f⎻" 'OR_f_minus r = (fun12 __ (or_f_minus _ _) r).
-interpretation "o-relation f*" 'OR_f_star r = (fun12 __ (or_f_star _ _) r).
+interpretation "o-relation f⎻*" 'OR_f_minus_star r = (fun12 ?? (or_f_minus_star ? ?) r).
+interpretation "o-relation f⎻" 'OR_f_minus r = (fun12 ?? (or_f_minus ? ?) r).
+interpretation "o-relation f*" 'OR_f_star r = (fun12 ?? (or_f_star ? ?) r).
 
 definition or_prop1 : ∀P,Q:OAlgebra.∀F:ORelation_setoid P Q.∀p,q.
    (F p ≤ q) = (p ≤ F* q).
@@ -286,8 +287,7 @@ constructor 1;
     apply or_prop3;
   ]
 | intros; split; simplify; 
-   [3: unfold arrows1_of_ORelation_setoid;
-         apply ((†e)‡(†e1));
+   [3: unfold arrows1_of_ORelation_setoid; apply ((†e)‡(†e1));
    |1: apply ((†e)‡(†e1));
    |2,4: apply ((†e1)‡(†e));]]
 qed.