update in basuc_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpce_etc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce_etc.ma
index 70370b58baa113e86732fc853d974b0e712bc4b8..2a899b25e2da3e5aad7a64ee35bbaa412c1c652c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce_etc.ma
@@ -1,19 +1,40 @@
+
 include "basic_2/dynamic/cnv_cpce.ma".
 
-lemma pippo (h) (a) (G) (L0):
-      ∀T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
-      ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
-      ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
-      ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
-#h #a #G #L0 * *
-[ #s #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
+definition dropable_bi: predicate … ≝
+           λR. ∀L1,L2. L1 ⪤[R] L2 → ∀b,f. 𝐔⦃f⦄ →
+           ∀K1. ⇩*[b,f] L1 ≘ K1 → ∀K2. ⇩*[b,f] L2 ≘ K2 → K1 ⪤[R] K2.
+
+definition IH (h) (a): relation3 genv lenv term ≝
+           λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
+           ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
+           ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
+           ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
+
+lemma pippo_aux (h) (a) (G0) (L0) (T0):
+                (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH h a G L T) →
+                IH h a G0 L0 T0.
+#h #a #G0 #L0 * *
+[ #s #_ #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
   elim (cpm_inv_sort1 … HX1) -HX1 #H #Hn destruct
   lapply (cpce_inv_sort_sn … HX2) -HX2 #H destruct
   /3 width=3 by cpce_sort, cpm_sort, ex2_intro/
-| #i #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
-  elim (drops_F_uni L0 i)
-  [
-  | *
+| #i #IH #Hi #n #X1 #HX1 #X2 #HX2 #L1 #HL01
+  elim (cnv_inv_lref_drops … Hi) -Hi #I #K0 #W0 #HLK0 #HW0
+  elim (lpr_drops_conf … HLK0 … HL01) [| // ] #Y1 #H1 #HLK1
+  elim (lex_inv_pair_sn … H1) -H1 #K1 #W1 #HK01 #HW01 #H destruct
+  elim (cpce_inv_lref_sn_drops … HX2 … HLK0) -HX2 *
+  [ #HI #H destruct
+    elim (cpm_inv_lref1_drops … HX1) -HX1 *
+    [ #H1 #H2 destruct -HW0 -HLK0 -IH
+      @(ex2_intro … (#i)) [| // ]
+      @cpce_zero_drops #n #p #Y1 #X1 #V1 #U1 #HLY1 #HWU1
+      lapply (drops_mono … HLY1 … HLK1) -L1 #H2 destruct
+      /4 width=12 by lpr_cpms_trans, cpms_step_sn/
+    | #Y0 #W0 #W1 #HLY0 #HW01 #HWX1 -HI -HW0 -IH
+      lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
+      @(ex2_intro … X1) [| /2 width=6 by cpm_delta_drops/ ]
+
 
 (*
 lemma cpce_inv_eta_drops (h) (n) (G) (L) (i):