update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
index c63a1aa1209760964af4074632213d6ba11978b8..d47a061e37d92c57b1891819489146ee58b7c6e3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
@@ -12,9 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/lib/arith_2b.ma".
 include "basic_2/rt_computation/cpms_aaa.ma".
-include "basic_2/rt_computation/lprs_cpms.ma".
 include "basic_2/dynamic/cnv.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
@@ -22,8 +20,8 @@ include "basic_2/dynamic/cnv.ma".
 (* Forward lemmas on atomic arity assignment for terms **********************)
 
 (* Basic_2A1: uses: snv_fwd_aaa *)
-lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
-#a #h #G #L #T #H elim H -G -L -T
+lemma cnv_fwd_aaa (h) (a): ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ∃A. ❪G,L❫ ⊢ T ⁝ A.
+#h #a #G #L #T #H elim H -G -L -T
 [ /2 width=2 by aaa_sort, ex_intro/
 | #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
 | #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
@@ -45,37 +43,39 @@ qed-.
 
 (* Forward lemmas with t_bound rt_transition for terms **********************)
 
-lemma cnv_fwd_cpm_SO (a) (h) (G) (L):
-      â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ T ![a, h] â\86\92 â\88\83U. â¦\83G,Lâ¦\84 ⊢ T ➡[1,h] U.
-#a #h #G #L #T #H
+lemma cnv_fwd_cpm_SO (h) (a) (G) (L):
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\88\83U. â\9dªG,Lâ\9d« ⊢ T ➡[1,h] U.
+#h #a #G #L #T #H
 elim (cnv_fwd_aaa … H) -H #A #HA
 /2 width=2 by aaa_cpm_SO/
 qed-.
 
 (* Forward lemmas with t_bound rt_computation for terms *********************)
 
-lemma cnv_fwd_cpms_total (a) (h) (n) (G) (L):
-      â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ T ![a, h] â\86\92 â\88\83U. â¦\83G,Lâ¦\84 ⊢ T ➡*[n,h] U.
-#a #h #n #G #L #T #H
+lemma cnv_fwd_cpms_total (h) (a) (n) (G) (L):
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\88\83U. â\9dªG,Lâ\9d« ⊢ T ➡*[n,h] U.
+#h #a #n #G #L #T #H
 elim (cnv_fwd_aaa … H) -H #A #HA
 /2 width=2 by cpms_total_aaa/
 qed-.
 
-(* Advanced inversion lemmas ************************************************)
-
-lemma cnv_inv_appl_pred (a) (h) (G) (L):
-      ∀V,T. ⦃G, L⦄ ⊢ ⓐV.T ![yinj a, h] →
-      ∃∃p,W0,U0. ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
-                   ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[↓a, h] ⓛ{p}W0.U0.
-#a #h #G #L #V #T #H
-elim (cnv_inv_appl … H) -H #n #p #W #U #Ha #HV #HT #HVW #HTU
-lapply (ylt_inv_inj … Ha) -Ha #Ha
-elim (cnv_fwd_aaa … HT) #A #HA
-elim (cpms_total_aaa h … (a-↑n) … (ⓛ{p}W.U))
-[|*: /2 width=8 by cpms_aaa_conf/ ] -HA #X #HU0
-elim (cpms_inv_abst_sn … HU0) #W0 #U0 #HW0 #_ #H destruct
-lapply (cpms_trans … HVW … HW0) -HVW -HW0 #HVW0
-lapply (cpms_trans … HTU … HU0) -HTU -HU0
->(arith_m2 … Ha) -Ha #HTU0
-/2 width=5 by ex4_3_intro/
+lemma cnv_fwd_cpms_abst_dx_le (h) (a) (G) (L) (W) (p):
+      ∀T. ❪G,L❫ ⊢ T ![h,a] →
+      ∀n1,U1. ❪G,L❫ ⊢ T ➡*[n1,h] ⓛ[p]W.U1 → ∀n2. n1 ≤ n2 →
+      ∃∃U2. ❪G,L❫ ⊢ T ➡*[n2,h] ⓛ[p]W.U2 & ❪G,L.ⓛW❫ ⊢ U1 ➡*[n2-n1,h] U2.
+#h #a #G #L #W #p #T #H
+elim (cnv_fwd_aaa … H) -H #A #HA
+/2 width=2 by cpms_abst_dx_le_aaa/
 qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cnv_appl_ge (h) (a) (n1) (p) (G) (L):
+      ∀n2. n1 ≤ n2 → ad a n2 →
+      ∀V. ❪G,L❫ ⊢ V ![h,a] → ∀T. ❪G,L❫ ⊢ T ![h,a] →
+      ∀X. ❪G,L❫ ⊢ V ➡*[1,h] X → ∀W. ❪G,L❫ ⊢ W ➡*[h] X →
+      ∀U. ❪G,L❫ ⊢ T ➡*[n1,h] ⓛ[p]W.U → ❪G,L❫ ⊢ ⓐV.T ![h,a].
+#h #a #n1 #p #G #L #n2 #Hn12 #Ha #V #HV #T #HT #X #HVX #W #HW #X #HTX
+elim (cnv_fwd_cpms_abst_dx_le  … HT … HTX … Hn12) #U #HTU #_ -n1
+/4 width=11 by cnv_appl, cpms_bind, cpms_cprs_trans/
+qed.