ok

[helm.git] / helm / software / matita / dama / premetric_lattice.ma

diff --git a/helm/software/matita/dama/premetric_lattice.ma b/helm/software/matita/dama/premetric_lattice.ma
index 61c4b826d7453e9f3785b14a2e9ba139775fac1b..42d00fd268a81a48cd67dc2c40baa974a372111b 100644 (file)
--- a/helm/software/matita/dama/premetric_lattice.ma
+++ b/helm/software/matita/dama/premetric_lattice.ma
@@ -49,12 +49,21 @@ include "lattice.ma".
 
 lemma lattice_of_pmlattice: ∀R: ogroup. pmlattice R → lattice.
 intros (R pml); apply (mk_lattice (apart_of_metric_space ? pml));
-[apply (join ? pml)|apply (meet ? pml)]
-intros (x y z); whd; intro H; whd in H; cases H (LE AP);
-[apply (prop2a ? pml pml x y);  |apply (prop2b ? pml pml x y); 
+[apply (join ? pml)|apply (meet ? pml)
+|3,4,5,6,7,8,9,10: intros (x y z); whd; intro H; whd in H; cases H (LE AP);]
+[apply (prop1b ? pml pml x);    |apply (prop1a ? pml pml x);
+|apply (prop2a ? pml pml x y);  |apply (prop2b ? pml pml x y); 
 |apply (prop3a ? pml pml x y z);|apply (prop3b ? pml pml x y z);
 |apply (prop4a ? pml pml x y);  |apply (prop4b ? pml pml x y);]
-apply ap_symmetric; assumption;
+try (apply ap_symmetric; assumption); intros 4 (x y z H); change with (0 < (δ y z));
+[ change in H with (0 < δ (x ∨ y) (x ∨ z));
+  apply (lt_le_transitive ???? H);  
+  apply (le0plus_le ???? (mpositive ? pml ??) (prop5 ? pml pml x y z));
+| change in H with (0 < δ (x ∧ y) (x ∧ z));
+  apply (lt_le_transitive ???? H);  
+  apply (le0plus_le ???? (mpositive ? pml (x∨y) (x∨z)));
+  apply (le_rewl ??? ? (plus_comm ???));
+  apply (prop5 ? pml pml);] 
 qed.
 
 coercion cic:/matita/premetric_lattice/lattice_of_pmlattice.con.
\ No newline at end of file