- matita: computed auto traces now include the "width" parameter

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / trace_isid.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_isid.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_isid.ma
index d87487c897fa098b1b59e56c107ce1c2fda70c75..6dce9e0a2fd8db60fa006cfbcf4d26fab5ad5291 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_isid.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/trace_isid.ma
@@ -12,15 +12,19 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/relations/isid_1.ma".
+include "ground_2/notation/relations/isidentity_1.ma".
 include "ground_2/relocation/trace_after.ma".
+include "ground_2/relocation/trace_sle.ma".
 
 (* RELOCATION TRACE *********************************************************)
 
 definition isid: predicate trace ≝ λcs. ∥cs∥ = |cs|.
 
 interpretation "test for identity (trace)"
-   'IsId cs = (isid cs).
+   'IsIdentity cs = (isid cs).
+
+definition t_reflexive: ∀S:Type[0]. predicate (trace → relation S) ≝
+                        λS,R. ∀a. ∃∃t. 𝐈⦃t⦄ & R t a a.
 
 (* Basic properties *********************************************************)
 
@@ -98,3 +102,13 @@ lemma after_inv_isid3: ∀t1,t2,t. t1 ⊚ t2 ≡ t → 𝐈⦃t⦄ → 𝐈⦃t1
 | #t1 #t2 #t #_ #_ #H elim (isid_inv_false … H)
 ]
 qed-.
+
+(* Forward on inclusion *****************************************************)
+
+lemma sle_isid1_fwd: ∀t1,t2. t1 ⊆ t2 → 𝐈⦃t1⦄ → t1 = t2.
+#t1 #t2 #H elim H -t1 -t2 //
+[ #t1 #t2 #_ #IH #H lapply (isid_inv_true … H) -H
+  #HT1 @eq_f2 // @IH @HT1 (**) (* full auto fails *)
+| #t1 #t2 #b #_ #_ #H elim (isid_inv_false … H)
+]
+qed-.