(* *)
(**************************************************************************)
-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 *********************************************************)
| #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-.