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 5667b7870030da075683c5fad3b339dcf7c8f9b1..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
@@ -20,8 +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/
@@ -43,39 +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-.
 
-lemma cnv_fwd_cpms_abst_dx_le (a) (h) (G) (L) (W) (p):
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![a,h] →
-      â\88\80n1,U1. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n1,h] â\93\9b{p}W.U1 → ∀n2. n1 ≤ n2 →
-      â\88\83â\88\83U2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n2,h] â\93\9b{p}W.U2 & â¦\83G,L.â\93\9bWâ¦\84 ⊢ U1 ➡*[n2-n1,h] U2.
-#a #h #G #L #W #p #T #H
+lemma cnv_fwd_cpms_abst_dx_le (h) (a) (G) (L) (W) (p):
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] →
+      â\88\80n1,U1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n1,h] â\93\9b[p]W.U1 → ∀n2. n1 ≤ n2 →
+      â\88\83â\88\83U2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n2,h] â\93\9b[p]W.U2 & â\9dªG,L.â\93\9bWâ\9d« ⊢ 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 (a) (h) (n1) (p) (G) (L):
-      ∀n2. n1 ≤ n2 → appl a n2 →
-      â\88\80V. â¦\83G,Lâ¦\84 â\8a¢ V ![a,h] â\86\92 â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![a,h] →
-      â\88\80X. â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡*[1,h] X â\86\92 â\88\80W. â¦\83G,Lâ¦\84 ⊢ W ➡*[h] X →
-      â\88\80U. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n1,h] â\93\9b{p}W.U â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.T ![a,h].
-#a #h #n1 #p #G #L #n2 #Hn12 #Ha #V #HV #T #HT #X #HVX #W #HW #X #HTX
+lemma cnv_appl_ge (h) (a) (n1) (p) (G) (L):
+      ∀n2. n1 ≤ n2 → ad a n2 →
+      â\88\80V. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] â\86\92 â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] →
+      â\88\80X. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡*[1,h] X â\86\92 â\88\80W. â\9dªG,Lâ\9d« ⊢ W ➡*[h] X →
+      â\88\80U. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n1,h] â\93\9b[p]W.U â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\93\90V.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.