- we proved that context-free reduction admits no one-step loops

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / grammar / term.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma b/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
index 46ba2cef2d91849d1c34bd8550e4e62a43e9741f..376061b70bb52cef59e3b11c08cb920ab6ba42ff 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
@@ -26,6 +26,8 @@ interpretation "sort (term)" 'Star k = (TAtom (Sort k)).
 
 interpretation "local reference (term)" 'LRef i = (TAtom (LRef i)).
 
+interpretation "global reference (term)" 'GRef p = (TAtom (GRef p)).
+
 interpretation "term construction (atomic)" 'SItem I = (TAtom I).
 
 interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
@@ -33,3 +35,32 @@ interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
 interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
 
 interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma discr_tpair_xy_x: ∀I,T,V. 𝕔{I} V. T = V → False.
+#I #T #V elim V -V
+[ #J #H destruct
+| #J #W #U #IHW #_ #H destruct
+(*
+ (generalize in match e1) -e1 >e0 normalize
+*) -I /2/ (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+]
+qed-.
+
+(* Basic_1: was: thead_x_y_y *)
+lemma discr_tpair_xy_y: ∀I,V,T. 𝕔{I} V. T = T → False.
+#I #V #T elim T -T
+[ #J #H destruct
+| #J #W #U #_ #IHU #H destruct -I V /2/ (**) (* destruct: the destucted equality is not erased *)
+]
+qed-.
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was: term_dec *)
+axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
+
+(* Basic_1: removed theorems 3:
+            not_void_abst not_abbr_void not_abst_void
+*)