update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma
index 6447e51ae8f635ca6977c2127b5ed611975ba36f..707ecb19d5afb8284fdf4441f10aa68a31a7e709 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/rt_transition/cpg_drops.ma".
-include "basic_2/rt_transition/cpt.ma".
+include "basic_2/rt_transition/cpt_fqu.ma".
 
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
 
@@ -44,3 +44,112 @@ lemma cpt_inv_lifts_bi (h) (n) (G):
       d_deliftable2_bi … lifts (λL. cpt h G L n).
 #h #n #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
 qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cpt_delta_drops (h) (n) (G):
+      ∀L,K,V,i. ⇩*[i] L ≘ K.ⓓV → ∀V2. ⦃G,K⦄ ⊢ V ⬆[h,n] V2 →
+      ∀W2. ⇧*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬆[h,n] W2.
+#h #n #G #L #K #V #i #HLK #V2 *
+/3 width=8 by cpg_delta_drops, ex2_intro/
+qed.
+
+lemma cpt_ell_drops (h) (n) (G):
+      ∀L,K,V,i. ⇩*[i] L ≘ K.ⓛV → ∀V2. ⦃G,K⦄ ⊢ V ⬆[h,n] V2 →
+      ∀W2. ⇧*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬆[h,↑n] W2.
+#h #n #G #L #K #V #i #HLK #V2 *
+/3 width=8 by cpg_ell_drops, ist_succ, ex2_intro/
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma cpt_inv_atom_sn_drops (h) (n) (I) (G) (L):
+      ∀X2. ⦃G,L⦄ ⊢ ⓪{I} ⬆[h,n] X2 →
+      ∨∨ ∧∧ X2 = ⓪{I} & n = 0
+       | ∃∃s. X2 = ⋆(⫯[h]s) & I = Sort s & n = 1
+       | ∃∃K,V,V2,i. ⇩*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ⬆[h,n] V2 & ⇧*[↑i] V2 ≘ X2 & I = LRef i
+       | ∃∃m,K,V,V2,i. ⇩*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ⬆[h,m] V2 & ⇧*[↑i] V2 ≘ X2 & I = LRef i & n = ↑m.
+#h #n #I #G #L #X2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *
+[ #H1 #H2 destruct
+  /3 width=1 by or4_intro0, conj/
+| #s #H1 #H2 #H3 destruct
+  /3 width=3 by or4_intro1, ex3_intro/
+| #cV #i #K #V1 #V2 #HLK #HV12 #HVT2 #H1 #H2 destruct
+  /4 width=8 by ex4_4_intro, ex2_intro, or4_intro2/
+| #cV #i #K #V1 #V2 #HLK #HV12 #HVT2 #H1 #H2 destruct
+  elim (ist_inv_plus_SO_dx … H2) -H2
+  /4 width=10 by ex5_5_intro, ex2_intro, or4_intro3/
+]
+qed-.
+
+lemma cpt_inv_lref_sn_drops (h) (n) (G) (L) (i):
+      ∀X2. ⦃G,L⦄ ⊢ #i ⬆[h,n] X2 →
+      ∨∨ ∧∧ X2 = #i & n = 0
+       | ∃∃K,V,V2. ⇩*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ⬆[h,n] V2 & ⇧*[↑i] V2 ≘ X2
+       | ∃∃m,K,V,V2. ⇩*[i] L ≘ K. ⓛV & ⦃G,K⦄ ⊢ V ⬆[h,m] V2 & ⇧*[↑i] V2 ≘ X2 & n = ↑m.
+#h #n #G #L #i #X2 * #c #Hc #H elim (cpg_inv_lref1_drops … H) -H *
+[ #H1 #H2 destruct
+  /3 width=1 by or3_intro0, conj/
+| #cV #K #V1 #V2 #HLK #HV12 #HVT2 #H destruct
+  /4 width=6 by ex3_3_intro, ex2_intro, or3_intro1/
+| #cV #K #V1 #V2 #HLK #HV12 #HVT2 #H destruct
+  elim (ist_inv_plus_SO_dx … H) -H
+  /4 width=8 by ex4_4_intro, ex2_intro, or3_intro2/
+]
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+fact cpt_fwd_plus_aux (h) (n) (G) (L):
+     ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ∀n1,n2. n1+n2 = n →
+     ∃∃T. ⦃G,L⦄ ⊢ T1 ⬆[h,n1] T & ⦃G,L⦄ ⊢ T ⬆[h,n2] T2.
+#h #n #G #L #T1 #T2 #H @(cpt_ind … H) -G -L -T1 -T2 -n
+[ #I #G #L #n1 #n2 #H
+  elim (plus_inv_O3 … H) -H #H1 #H2 destruct
+  /2 width=3 by ex2_intro/
+| #G #L #s #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct /2 width=3 by ex2_intro/
+  | #n1 #H1 #H elim (plus_inv_O3 … H) -H #H2 #H3 destruct
+    /2 width=3 by ex2_intro/
+  ]
+| #n #G #K #V1 #V2 #W2 #_ #IH #HVW2 #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #V #HV1 #HV2
+  elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+  /5 width=11 by cpt_lifts_bi, cpt_delta, drops_refl, drops_drop, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #HV12 #IH #HVW2 #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct -IH /3 width=3 by cpt_ell, ex2_intro/
+  | #n1 #H1 #H2 destruct -HV12
+    elim (IH n1) [|*: // ] -IH #V #HV1 #HV2
+    elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+    /5 width=11 by cpt_lifts_bi, cpt_ell, drops_refl, drops_drop, ex2_intro/
+  ]
+| #n #I #G #K #T2 #U2 #i #_ #IH #HTU2 #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  elim (lifts_total T 𝐔❴↑O❵) #U #HTU
+  /5 width=11 by cpt_lifts_bi, cpt_lref, drops_refl, drops_drop, ex2_intro/
+| #n #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ #IHT #n1 #n2 #H destruct
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpt_bind, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ #IHT #n1 #n2 #H destruct
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpt_appl, ex2_intro/
+| #n #G #L #U1 #U2 #T1 #T2 #_ #_ #IHU #IHT #n1 #n2 #H destruct
+  elim IHU [|*: // ] -IHU #U #HU1 #HU2
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpt_cast, ex2_intro/
+| #n #G #L #U1 #U2 #T #HU12 #IH #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct -IH /3 width=4 by cpt_ee, cpt_cast, ex2_intro/
+  | #n1 #H1 #H2 destruct -HU12
+    elim (IH n1) [|*: // ] -IH #U #HU1 #HU2
+    /3 width=3 by cpt_ee, ex2_intro/
+  ]
+]
+qed-.
+
+lemma cpt_fwd_plus (h) (n1) (n2) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n1+n2] T2 →
+      ∃∃T. ⦃G,L⦄ ⊢ T1 ⬆[h,n1] T & ⦃G,L⦄ ⊢ T ⬆[h,n2] T2.
+/2 width=3 by cpt_fwd_plus_aux/ qed-.