some added lemmas removed from auto

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_conversion / cpce_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/cpce_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/cpce_drops.ma
index 49bf1e88567369b3f0ddc29ccca205b3bf020fca..985f9f8f4e7cc98d1aa0c857de43e775449a9f8c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/cpce_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/cpce_drops.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "static_2/relocation/drops.ma".
+include "static_2/relocation/lifts_lifts.ma".
 include "basic_2/rt_conversion/cpce.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL ETA-CONVERSION FOR TERMS **********************)
@@ -22,8 +23,8 @@ include "basic_2/rt_conversion/cpce.ma".
 lemma cpce_eta_drops (h) (n) (G) (K):
       ∀p,W,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
       ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
-      â\88\80i,L. â¬\87*[i] L ≘ K.ⓛW →
-      â\88\80W2. â¬\86*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬌η[h] +ⓛW2.ⓐ#0.#↑i.
+      â\88\80i,L. â\87©*[i] L ≘ K.ⓛW →
+      â\88\80W2. â\87§*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬌η[h] +ⓛW2.ⓐ#0.#↑i.
 #h #n #G #K #p #W #V1 #U #HWU #V2 #HV12 #i elim i -i
 [ #L #HLK #W2 #HVW2
   >(drops_fwd_isid … HLK) -L [| // ] /2 width=8 by cpce_eta/
@@ -35,7 +36,7 @@ lemma cpce_eta_drops (h) (n) (G) (K):
 qed.
 
 lemma cpce_zero_drops (h) (G):
-      â\88\80i,L. (â\88\80n,p,K,W,V,U. â¬\87*[i] L ≘ K.ⓛW → ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V.U → ⊥) →
+      â\88\80i,L. (â\88\80n,p,K,W,V,U. â\87©*[i] L ≘ K.ⓛW → ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V.U → ⊥) →
       ⦃G,L⦄ ⊢ #i ⬌η[h] #i.
 #h #G #i elim i -i
 [ * [ #_ // ] #L #I #Hi
@@ -44,3 +45,46 @@ lemma cpce_zero_drops (h) (G):
   /5 width=8 by cpce_lref, drops_drop/
 ]
 qed.
+
+(* Inversion lemmas with uniform slicing for local environments *************)
+
+lemma cpce_inv_lref_sn_drops (h) (G) (i) (L):
+      ∀X2. ⦃G,L⦄ ⊢ #i ⬌η[h] X2 →
+      ∀I,K. ⇩*[i] L ≘ K.ⓘ{I} →
+      ∨∨ ∧∧ ∀n,p,W,V,U. I = BPair Abst W → ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V.U → ⊥ & #i = X2
+       | ∃∃n,p,W,V1,V2,W2,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U & ⦃G,K⦄ ⊢ V1 ⬌η[h] V2
+                           & ⇧*[↑i] V2 ≘ W2 & I = BPair Abst W & +ⓛW2.ⓐ#0.#(↑i) = X2.
+#h #G #i elim i -i
+[ #L #X2 #HX2 #I #K #HLK
+  lapply (drops_fwd_isid … HLK ?) -HLK [ // ] #H destruct
+  /2 width=1 by cpce_inv_zero_sn/
+| #i #IH #L0 #X0 #HX0 #J #K #H0
+  elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct
+  elim (cpce_inv_lref_sn … HX0) -HX0 #X2 #HX2 #HX20
+  elim (IH … HX2 … HLK) -IH -I -L *
+  [ #HJ #H destruct
+    lapply (lifts_inv_lref1_uni … HX20) -HX20 #H destruct
+    /4 width=7 by or_introl, conj/
+  | #n #p #W #V1 #V2 #W2 #U #HWU #HV12 #HVW2 #H1 #H2 destruct
+    elim (lifts_inv_bind1 … HX20) -HX20 #X2 #X #HWX2 #HX #H destruct
+    elim (lifts_inv_flat1 … HX) -HX #X0 #X1 #H0 #H1 #H destruct
+    lapply (lifts_inv_push_zero_sn … H0) -H0 #H destruct
+    elim (lifts_inv_push_succ_sn … H1) -H1 #j #Hj #H destruct
+    lapply (lifts_inv_lref1_uni … Hj) -Hj #H destruct
+    /4 width=12 by lifts_trans_uni, ex5_7_intro, or_intror/
+  ]
+]
+qed-.
+
+lemma cpce_inv_zero_sn_drops (h) (G) (i) (L):
+      ∀X2. ⦃G,L⦄ ⊢ #i ⬌η[h] X2 →
+      ∀I,K. ⇩*[i] L ≘ K.ⓘ{I} →
+      (∀n,p,W,V,U. I = BPair Abst W → ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V.U → ⊥) →
+      #i = X2.
+#h #G #i #L #X2 #HX2 #I #K #HLK #HI
+elim (cpce_inv_lref_sn_drops … HX2 … HLK) -L *
+[ #_ #H //
+| #n #p #W #V1 #V2 #W2 #U #HWU #_ #_ #H destruct
+  elim (HI … HWU) -n -p -K -X2 -V1 -V2 -W2 -U -i //
+]
+qed-.