update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cnuw_cnuw.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma
index 0249a95e07c4e3c8683234e727c8736f1c980897..76c7cb96405c3224c8aac217b8c57b613e1d394a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_cnuw.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/cnuw.ma".
+include "basic_2/rt_computation/cnuw_simple.ma".
+include "basic_2/rt_computation/cnuw_drops.ma".
 include "basic_2/rt_computation/cprs_tweq.ma".
 include "basic_2/rt_computation/lprs_cpms.ma".
 
@@ -21,7 +22,7 @@ include "basic_2/rt_computation/lprs_cpms.ma".
 (* Advanced inversion lemmas ************************************************)
 
 lemma cnuw_inv_abbr_pos (h) (G) (L):
-      â\88\80V,T. â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
+      â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] +ⓓV.T → ⊥.
 #h #G #L #V #T1 #H
 elim (cprs_abbr_pos_twneq h G L V T1) #T2 #HT12 #HnT12
 /3 width=2 by/
@@ -29,7 +30,7 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma cnuw_abbr_neg (h) (G) (L): â\88\80V,T. â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
+lemma cnuw_abbr_neg (h) (G) (L): â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] -ⓓV.T.
 #h #G #L #V1 #T1 #n #X #H
 elim (cpms_inv_abbr_sn_dx … H) -H *
 [ #V2 #T2 #_ #_ #H destruct /1 width=1 by tweq_abbr_neg/
@@ -37,15 +38,69 @@ elim (cpms_inv_abbr_sn_dx … H) -H *
 ]
 qed.
 
-lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â¦\83G,Lâ¦\84 â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] â\93\9b{p}W.T.
+lemma cnuw_abst (h) (p) (G) (L): â\88\80W,T. â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] â\93\9b[p]W.T.
 #h #p #G #L #W1 #T1 #n #X #H
 elim (cpms_inv_abst_sn … H) -H #W2 #T2 #_ #_ #H destruct
 /1 width=1 by tweq_abst/
 qed.
 
 lemma cnuw_cpms_trans (h) (n) (G) (L):
-      â\88\80T1. â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T1 →
-      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T2.
+      â\88\80T1. â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T1 →
+      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T2.
 #h #n1 #G #L #T1 #HT1 #T2 #HT12 #n2 #T3 #HT23
 /4 width=5 by cpms_trans, tweq_canc_sn/
 qed-.
+
+lemma cnuw_dec_ex (h) (G) (L):
+      ∀T1. ∨∨ ❪G,L❫ ⊢ ➡𝐍𝐖*[h] T1
+            | ∃∃n,T2. ❪G,L❫ ⊢ T1 ➡*[n,h] T2 & (T1 ≅ T2 → ⊥).
+#h #G #L #T1 elim T1 -T1 *
+[ #s /3 width=5 by cnuw_sort, or_introl/
+| #i elim (drops_F_uni L i)
+  [ /3 width=7 by cnuw_atom_drops, or_introl/
+  | * * [ #I | * #V ] #K #HLK
+    [ /3 width=8 by cnuw_unit_drops, or_introl/
+    | elim (lifts_total V 𝐔❨↑i❩) #W #HVW
+      @or_intror @(ex2_2_intro … W) [1,2: /2 width=7 by cpms_delta_drops/ ] #H
+      lapply (tweq_inv_lref_sn … H) -H #H destruct
+      /2 width=5 by lifts_inv_lref2_uni_lt/
+    | elim (lifts_total V 𝐔❨↑i❩) #W #HVW
+      @or_intror @(ex2_2_intro … W) [1,2: /2 width=7 by cpms_ell_drops/ ] #H
+      lapply (tweq_inv_lref_sn … H) -H #H destruct
+      /2 width=5 by lifts_inv_lref2_uni_lt/
+    ]
+  ]
+| #l /3 width=5 by cnuw_gref, or_introl/
+| #p * [ cases p ] #V1 #T1 #_ #_
+  [ elim (cprs_abbr_pos_twneq h G L V1 T1) #T2 #HT12 #HnT12
+    /4 width=4 by ex2_2_intro, or_intror/
+  | /3 width=5 by cnuw_abbr_neg, or_introl/
+  | /3 width=5 by cnuw_abst, or_introl/
+  ]
+| * #V1 #T1 #_ #IH
+  [ elim (simple_dec_ex T1) [ #HT1 | * #p * #W1 #U1 #H destruct ]
+    [ elim IH -IH
+      [ /3 width=6 by cnuw_appl_simple, or_introl/
+      | * #n #T2 #HT12 #HnT12 -HT1
+        @or_intror @(ex2_2_intro … n (ⓐV1.T2)) [ /2 width=1 by cpms_appl_dx/ ] #H
+        lapply (tweq_inv_appl_bi … H) -H /2 width=1 by/
+      ]
+    | elim (lifts_total V1 𝐔❨1❩) #X1 #HVX1
+      @or_intror @(ex2_2_intro … (ⓓ[p]W1.ⓐX1.U1)) [1,2: /2 width=3 by cpms_theta/ ] #H
+      elim (tweq_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
+    | @or_intror @(ex2_2_intro … (ⓓ[p]ⓝW1.V1.U1)) [1,2: /2 width=2 by cpms_beta/ ] #H
+      elim (tweq_inv_appl_sn … H) -H #X1 #X2 #_ #H destruct
+    ]
+  | @or_intror @(ex2_2_intro … T1) [1,2: /2 width=2 by cpms_eps/ ] #H
+    /2 width=4 by tweq_inv_cast_xy_y/
+  ]
+]
+qed-.
+
+lemma cnuw_dec (h) (G) (L): ∀T. Decidable (❪G,L❫ ⊢ ➡𝐍𝐖*[h] T).
+#h #G #L #T1
+elim (cnuw_dec_ex h G L T1)
+[ /2 width=1 by or_introl/
+| * #n #T2 #HT12 #nT12 /4 width=2 by or_intror/
+]
+qed-.