initial properies of the "same top term constructor" predicate

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / csn.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn.ma
index b6ebc547f2e55eaac75c341b7a588d1f7e8046ed..043fa9a277e25087e892c2805158f7b480052a7d 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "Basic_2/reducibility/cpr.ma".
-include "Basic_2/computation/acp.ma".
+include "Basic_2/reducibility/cnf.ma".
 
 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
 
@@ -21,8 +21,65 @@ definition csn: lenv → predicate term ≝ λL. SN … (cpr L) (eq …).
 
 interpretation
    "context-sensitive strong normalization (term)"
-   'SN L T = (csn L T). 
+   'SN L T = (csn L T).
+
+(* Basic eliminators ********************************************************)
+
+lemma csn_ind: ∀L. ∀R:predicate term.
+               (∀T1. L ⊢ ⬇* T1 →
+                     (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → R T2) →
+                     R T1
+               ) →
+               ∀T. L ⊢ ⬇* T → R T.
+#L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
+@H0 -H0 /3 width=1/ -IHT1 /4 width=1/
+qed-.
 
 (* Basic properties *********************************************************)
 
-axiom csn_acp: acp cpr (eq …) (csn …).
+(* Basic_1: was: sn3_pr2_intro *)
+lemma csn_intro: ∀L,T1.
+                 (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇* T2) → L ⊢ ⬇* T1.
+#L #T1 #H
+@(SN_intro … H)
+qed.
+
+(* Basic_1: was: sn3_nf2 *)
+lemma csn_cnf: ∀L,T. L ⊢ 𝐍[T] → L ⊢ ⬇* T.
+/2 width=1/ qed.
+
+lemma csn_cpr_trans: ∀L,T1. L ⊢ ⬇* T1 → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ ⬇* T2.
+#L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+@csn_intro #T #HLT2 #HT2
+elim (term_eq_dec T1 T2) #HT12
+[ -IHT1 -HLT12 destruct /3 width=1/
+| -HT1 -HT2 /3 width=4/
+qed.
+
+(* Basic_1: was: sn3_cast *)
+lemma csn_cast: ∀L,W. L ⊢ ⬇* W → ∀T. L ⊢ ⬇* T → L ⊢ ⬇* ⓣW. T.
+#L #W #HW elim HW -W #W #_ #IHW #T #HT @(csn_ind … HT) -T #T #HT #IHT
+@csn_intro #X #H1 #H2
+elim (cpr_inv_cast1 … H1) -H1
+[ * #W0 #T0 #HLW0 #HLT0 #H destruct
+  elim (eq_false_inv_tpair_sn … H2) -H2
+  [ /3 width=3/
+  | -HLW0 * #H destruct /3 width=1/ 
+  ]
+| /3 width=3/
+]
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+fact csn_fwd_flat_dx_aux: ∀L,U. L ⊢ ⬇* U → ∀I,V,T. U = ⓕ{I} V. T → L ⊢ ⬇* T.
+#L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+@csn_intro #T2 #HLT2 #HT2
+@(IH (ⓕ{I} V. T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
+qed.
+
+(* Basic_1: was: sn3_gen_flat *)
+lemma csn_fwd_flat_dx: ∀I,L,V,T. L ⊢ ⬇* ⓕ{I} V. T → L ⊢ ⬇* T.
+/2 width=5/ qed-.
+
+(* Basic_1: removed theorems 3: sn3_gen_cflat sn3_cflat sn3_bind *)