update in basic_2 and ground_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpm_tdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_tdeq.ma
index 0b15ef8138d94577385c8a7e01105bf5d148e8bc..ed7d341d434d72b9b49e48688ee7c2af8cef1aba 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_tdeq.ma
@@ -19,12 +19,32 @@ include "basic_2/rt_transition/cpm_drops.ma".
 
 (* Inversion lemmas with degree-based equivalence for terms *****************)
 
-lemma cpm_tdeq_inv_lref (n) (h) (o) (G) (L) (i):
-                        ∀X.  ⦃G, L⦄ ⊢ #i ➡[n,h] X → #i ≛[h,o] X →
-                        ∧∧ X = #i & n = 0.
+lemma cpm_tdeq_inv_lref_sn (n) (h) (o) (G) (L) (i):
+                           ∀X.  ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛[h,o] X →
+                           ∧∧ X = #i & n = 0.
 #n #h #o #G #L #i #X #H1 #H2
 lapply (tdeq_inv_lref1 … H2) -H2 #H destruct
 elim (cpm_inv_lref1_drops … H1) -H1 // * [| #m ]
 #K #V1 #V2 #_ #_ #H -V1
 elim (lifts_inv_lref2_uni_lt … H) -H //
 qed-.
+
+lemma cpm_tdeq_inv_atom_sn (n) (h) (o) (I) (G) (L):
+                           ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛[h,o] X →
+                           ∨∨ ∧∧ X = ⓪{I} & n = 0
+                            | ∃∃s. X = ⋆(next h s) & I = Sort s & n = 1 & deg h o s 0.
+#n #h #o * #s #G #L #X #H1 #H2
+[ elim (cpm_inv_sort1 … H1) -H1
+  cases n -n [| #n ] #H #Hn destruct
+  [ /3 width=1 by or_introl, conj/
+  | elim (tdeq_inv_sort1 … H2) -H2 #x #d #Hs
+    <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n #Hx #H destruct
+    lapply (deg_next … Hs) #H
+    lapply (deg_mono … H Hx) -H -Hx #Hd
+    lapply (pred_inv_fix_sn … Hd) -Hd #H destruct
+    /3 width=4 by refl, ex4_intro, or_intror/
+  ]
+| elim (cpm_tdeq_inv_lref_sn … H1 H2) -H1 -H2 /3 width=1 by or_introl, conj/
+| elim (cpm_inv_gref1 … H1) -H1 -H2 /3 width=1 by or_introl, conj/
+]
+qed-.