X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fdama%2Fmetric_lattice.ma;h=f0242da284896e612f5774aa801bc881a9606ff8;hb=cf07c50b03a49344eb4cbe2e1bc18fcef880b9e9;hp=a4ca3b4f4b6029d692b618aae05eee9438190230;hpb=39c55604f8114e2e8f9f9769acd328de8f19c7e4;p=helm.git

diff --git a/helm/software/matita/dama/metric_lattice.ma b/helm/software/matita/dama/metric_lattice.ma
index a4ca3b4f4..f0242da28 100644
--- a/helm/software/matita/dama/metric_lattice.ma
+++ b/helm/software/matita/dama/metric_lattice.ma
@@ -12,20 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/metric_lattice/".
-
 include "metric_space.ma".
 include "lattice.ma".
 
-record mlattice_ (R : ogroup) : Type ≝ {
+record mlattice_ (R : todgroup) : Type ≝ {
   ml_mspace_: metric_space R;
   ml_lattice:> lattice;
-  ml_with_: ms_carr ? ml_mspace_ = ap_carr (l_carr ml_lattice)
+  ml_with: ms_carr ? ml_mspace_ = Type_OF_lattice ml_lattice 
 }.
 
 lemma ml_mspace: ∀R.mlattice_ R → metric_space R.
-intros (R ml); apply (mk_metric_space R ml); unfold Type_OF_mlattice_;
-cases (ml_with_ ? ml); simplify;
+intros  (R ml); apply (mk_metric_space R (Type_OF_mlattice_ ? ml));
+unfold Type_OF_mlattice_; cases (ml_with ? ml); simplify;
 [apply (metric ? (ml_mspace_ ? ml));|apply (mpositive ? (ml_mspace_ ? ml));
 |apply (mreflexive ? (ml_mspace_ ? ml));|apply (msymmetric ? (ml_mspace_ ? ml));
 |apply (mtineq ? (ml_mspace_ ? ml))]
@@ -33,24 +31,27 @@ qed.
 
 coercion cic:/matita/metric_lattice/ml_mspace.con.
 
-record is_mlattice (R : ogroup) (ml: mlattice_ R) : Type ≝ {
-  ml_prop1: ∀a,b:ml. 0 < δ a b → a # b;
-  ml_prop2: ∀a,b,c:ml. δ (a∨b) (a∨c) + δ (a∧b) (a∧c) ≤ δ b c
-}.
-
-record mlattice (R : ogroup) : Type ≝ {
+alias symbol "plus" = "Abelian group plus".
+alias symbol "leq" = "Excess less or equal than".
+record mlattice (R : todgroup) : Type ≝ {
   ml_carr :> mlattice_ R;
-  ml_props:> is_mlattice R ml_carr
+  ml_prop1: ∀a,b:ml_carr. 0 < δ a b → a # b;
+  ml_prop2: ∀a,b,c:ml_carr. δ (a∨b) (a∨c) + δ (a∧b) (a∧c) ≤ (δ b c)
 }.
 
+interpretation "Metric lattice leq" 'leq a b = 
+  (cic:/matita/excess/le.con (cic:/matita/metric_lattice/excess_OF_mlattice1.con _ _) a b). 
+interpretation "Metric lattice geq" 'geq a b = 
+  (cic:/matita/excess/le.con (cic:/matita/metric_lattice/excess_OF_mlattice.con _ _) a b). 
+
 lemma eq_to_ndlt0: ∀R.∀ml:mlattice R.∀a,b:ml. a ≈ b → ¬ 0 < δ a b.
-intros (R ml a b E); intro H; apply E; apply (ml_prop1 ?? ml);
+intros (R ml a b E); intro H; apply E; apply ml_prop1;
 assumption;
 qed.
 
 lemma eq_to_dzero: ∀R.∀ml:mlattice R.∀x,y:ml.x ≈ y → δ x y ≈ 0.
 intros (R ml x y H); intro H1; apply H; clear H; 
-apply (ml_prop1 ?? ml); split [apply mpositive] apply ap_symmetric;
+apply ml_prop1; split [apply mpositive] apply ap_symmetric;
 assumption;
 qed.
 
@@ -69,14 +70,13 @@ lemma meq_r: ∀R.∀ml:mlattice R.∀x,y,z:ml. x≈z → δy x ≈ δy z.
 intros; apply (eq_trans ???? (msymmetric ??y x));
 apply (eq_trans ????? (msymmetric ??z y)); apply meq_l; assumption;
 qed.
- 
 
 lemma dap_to_lt: ∀R.∀ml:mlattice R.∀x,y:ml. δ x y # 0 → 0 < δ x y.
 intros; split [apply mpositive] apply ap_symmetric; assumption;
 qed.
 
 lemma dap_to_ap: ∀R.∀ml:mlattice R.∀x,y:ml. δ x y # 0 → x # y.
-intros (R ml x y H); apply (ml_prop1 ?? ml); split; [apply mpositive;]
+intros (R ml x y H); apply ml_prop1; split; [apply mpositive;]
 apply ap_symmetric; assumption;
 qed.
 
@@ -84,22 +84,27 @@ qed.
 lemma le_mtri: 
   ∀R.∀ml:mlattice R.∀x,y,z:ml. x ≤ y → y ≤ z → δ x z ≈ δ x y + δ y z.
 intros (R ml x y z Lxy Lyz); apply le_le_eq; [apply mtineq]
-apply (le_transitive ????? (ml_prop2 ?? ml (y) ??)); 
+apply (le_transitive ????? (ml_prop2 ?? (y) ??)); 
 cut ( δx y+ δy z ≈ δ(y∨x) (y∨z)+ δ(y∧x) (y∧z)); [
   apply (le_rewr ??? (δx y+ δy z)); [assumption] apply le_reflexive]
-lapply (le_to_eqm ??? Lxy) as Dxm; lapply (le_to_eqm ??? Lyz) as Dym;
-lapply (le_to_eqj ??? Lxy) as Dxj; lapply (le_to_eqj ??? Lyz) as Dyj; clear Lxy Lyz;
-apply (Eq≈ (δ(x∧y) y + δy z)); [apply feq_plusr; apply (meq_l ????? Dxm);]
-apply (Eq≈ (δ(x∧y) (y∧z) + δy z)); [apply feq_plusr; apply (meq_r ????? Dym);]
-apply (Eq≈ (δ(x∧y) (y∧z) + δ(x∨y) z)); [apply feq_plusl; apply (meq_l ????? Dxj);]
-apply (Eq≈ (δ(x∧y) (y∧z) + δ(x∨y) (y∨z))); [apply feq_plusl; apply (meq_r ????? Dyj);]
+lapply (le_to_eqm y x Lxy) as Dxm; lapply (le_to_eqm z y Lyz) as Dym;
+lapply (le_to_eqj x y Lxy) as Dxj; lapply (le_to_eqj y z Lyz) as Dyj; clear Lxy Lyz;
+STOP
+apply (Eq≈ (δ(x∧y) y + δy z) (meq_l ????? Dxm));
+apply (Eq≈ (δ(x∧y) (y∧z) + δy z) (meq_r ????? Dym));
+apply (Eq≈ (δ(x∧y) (y∧z) + δ(y∨x) z));[
+  apply feq_plusl; apply meq_l; clear Dyj Dxm Dym; assumption]
+apply (Eq≈ (δ(x∧y) (y∧z) + δ(y∨x) (z∨y))); [
+  apply (feq_plusl ? (δ(x∧y) (y∧z)) ?? (meq_r ??? (y∨x) ? Dyj));]
 apply (Eq≈ ? (plus_comm ???));
-apply (Eq≈ (δ(y∨x) (y∨z)+ δ(x∧y) (y∧z))); [apply feq_plusr; apply (meq_l ????? (join_comm ???));]
+apply (Eq≈ (δ(y∨x) (y∨z)+ δ(x∧y) (y∧z)));[
+  apply feq_plusr; apply meq_r; apply (join_comm ??);]
 apply feq_plusl;
-apply (Eq≈ (δ(y∧x) (y∧z))); [apply (meq_l ????? (meet_comm ???));]
+apply (Eq≈ (δ(y∧x) (y∧z)) (meq_l ????? (meet_comm ??)));
 apply eq_reflexive;   
 qed.  
 
+
 (* 3.17 conclusione: δ x y ≈ 0 *)
 (* 3.20 conclusione: δ x y ≈ 0 *)
 (* 3.21 sup forte
@@ -109,4 +114,4 @@ qed.
 (* 3.22 sup debole (più piccolo dei maggioranti) *)
 (* 3.23 conclusion: δ x sup(...) ≈ 0 *)
 (* 3.25 vero nel reticolo e basta (niente δ) *)
-(* 3.36 conclusion: δ x y ≈ 0 *)
\ No newline at end of file
+(* 3.36 conclusion: δ x y ≈ 0 *)