milestone in basic_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..b99c4309c47dcfb56448a9df3e727f69110c1112 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
@@ -17,14 +17,30 @@ include "basic_2/rt_transition/cpm_drops.ma".
 
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
 
-(* Inversion lemmas with degree-based equivalence for terms *****************)
+(* Inversion lemmas with sort-irrelevant 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.
-#n #h #o #G #L #i #X #H1 #H2
+lemma cpm_tdeq_inv_lref_sn (n) (h) (G) (L) (i):
+                           ∀X.  ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛ X →
+                           ∧∧ X = #i & n = 0.
+#n #h #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) (I) (G) (L):
+                           ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛ X →
+                           ∨∨ ∧∧ X = ⓪{I} & n = 0
+                            | ∃∃s. X = ⋆(next h s) & I = Sort s & n = 1.
+#n #h * #s #G #L #X #H1 #H2
+[ elim (cpm_inv_sort1 … H1) -H1
+  cases n -n [| #n ] #H #Hn destruct -H2
+  [ /3 width=1 by or_introl, conj/
+  | <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n
+    /3 width=3 by ex3_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-.