X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpts.ma;h=9818e6d84254c54842d2d2525268e3cfc0615709;hp=24b6655b5fd7bb965f053fd8d31cc12195c594dc;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts.ma
index 24b6655b5..9818e6d84 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts.ma
@@ -29,51 +29,51 @@ interpretation
 
 lemma cpts_ind_sn (h) (G) (L) (T2) (Q:relation2 …):
                   Q 0 T2 →
-                  (∀n1,n2,T1,T. ⦃G,L⦄ ⊢ T1 ⬆[h,n1] T → ⦃G,L⦄ ⊢ T ⬆*[h,n2] T2 → Q n2 T → Q (n1+n2) T1) →
-                  ∀n,T1. ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2 → Q n T1.
+                  (∀n1,n2,T1,T. ❪G,L❫ ⊢ T1 ⬆[h,n1] T → ❪G,L❫ ⊢ T ⬆*[h,n2] T2 → Q n2 T → Q (n1+n2) T1) →
+                  ∀n,T1. ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 → Q n T1.
 #h #G #L #T2 #Q @ltc_ind_sn_refl //
 qed-.
 
 lemma cpts_ind_dx (h) (G) (L) (T1) (Q:relation2 …):
                   Q 0 T1 →
-                  (∀n1,n2,T,T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,n1] T → Q n1 T → ⦃G,L⦄ ⊢ T ⬆[h,n2] T2 → Q (n1+n2) T2) →
-                  ∀n,T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2 → Q n T2.
+                  (∀n1,n2,T,T2. ❪G,L❫ ⊢ T1 ⬆*[h,n1] T → Q n1 T → ❪G,L❫ ⊢ T ⬆[h,n2] T2 → Q (n1+n2) T2) →
+                  ∀n,T2. ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 → Q n T2.
 #h #G #L #T1 #Q @ltc_ind_dx_refl //
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma cpt_cpts (h) (G) (L):
-      ∀n,T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2.
+      ∀n,T1,T2. ❪G,L❫ ⊢ T1 ⬆[h,n] T2 → ❪G,L❫ ⊢ T1 ⬆*[h,n] T2.
 /2 width=1 by ltc_rc/ qed.
 
 lemma cpts_step_sn (h) (G) (L):
-      ∀n1,T1,T. ⦃G,L⦄ ⊢ T1 ⬆[h,n1] T →
-      ∀n2,T2. ⦃G,L⦄ ⊢ T ⬆*[h,n2] T2 → ⦃G,L⦄ ⊢ T1 ⬆*[h,n1+n2] T2.
+      ∀n1,T1,T. ❪G,L❫ ⊢ T1 ⬆[h,n1] T →
+      ∀n2,T2. ❪G,L❫ ⊢ T ⬆*[h,n2] T2 → ❪G,L❫ ⊢ T1 ⬆*[h,n1+n2] T2.
 /2 width=3 by ltc_sn/ qed-.
 
 lemma cpts_step_dx (h) (G) (L):
-      ∀n1,T1,T. ⦃G,L⦄ ⊢ T1 ⬆*[h,n1] T →
-      ∀n2,T2. ⦃G,L⦄ ⊢ T ⬆[h,n2] T2 → ⦃G,L⦄ ⊢ T1 ⬆*[h,n1+n2] T2.
+      ∀n1,T1,T. ❪G,L❫ ⊢ T1 ⬆*[h,n1] T →
+      ∀n2,T2. ❪G,L❫ ⊢ T ⬆[h,n2] T2 → ❪G,L❫ ⊢ T1 ⬆*[h,n1+n2] T2.
 /2 width=3 by ltc_dx/ qed-.
 
 lemma cpts_bind_dx (h) (n) (G) (L):
-      ∀V1,V2. ⦃G,L⦄ ⊢ V1 ⬆[h,0] V2 →
-      ∀I,T1,T2. ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬆*[h,n] T2 →
-      ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬆*[h,n] ⓑ{p,I}V2.T2.
+      ∀V1,V2. ❪G,L❫ ⊢ V1 ⬆[h,0] V2 →
+      ∀I,T1,T2. ❪G,L.ⓑ[I]V1❫ ⊢ T1 ⬆*[h,n] T2 →
+      ∀p. ❪G,L❫ ⊢ ⓑ[p,I]V1.T1 ⬆*[h,n] ⓑ[p,I]V2.T2.
 #h #n #G #L #V1 #V2 #HV12 #I #T1 #T2 #H #a @(cpts_ind_sn … H) -T1
 /3 width=3 by cpts_step_sn, cpt_cpts, cpt_bind/ qed.
 
 lemma cpts_appl_dx (h) (n) (G) (L):
-      ∀V1,V2. ⦃G,L⦄ ⊢ V1 ⬆[h,0] V2 →
-      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2 → ⦃G,L⦄ ⊢ ⓐV1.T1 ⬆*[h,n] ⓐV2.T2.
+      ∀V1,V2. ❪G,L❫ ⊢ V1 ⬆[h,0] V2 →
+      ∀T1,T2. ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 → ❪G,L❫ ⊢ ⓐV1.T1 ⬆*[h,n] ⓐV2.T2.
 #h #n #G #L #V1 #V2 #HV12 #T1 #T2 #H @(cpts_ind_sn … H) -T1
 /3 width=3 by cpts_step_sn, cpt_cpts, cpt_appl/
 qed.
 
 lemma cpts_ee (h) (n) (G) (L):
-      ∀U1,U2. ⦃G,L⦄ ⊢ U1 ⬆*[h,n] U2 →
-      ∀T. ⦃G,L⦄ ⊢ ⓝU1.T ⬆*[h,↑n] U2.
+      ∀U1,U2. ❪G,L❫ ⊢ U1 ⬆*[h,n] U2 →
+      ∀T. ❪G,L❫ ⊢ ⓝU1.T ⬆*[h,↑n] U2.
 #h #n #G #L #U1 #U2 #H @(cpts_ind_sn … H) -U1 -n
 [ /3 width=1 by cpt_cpts, cpt_ee/
 | #n1 #n2 #U1 #U #HU1 #HU2 #_ #T >plus_S1
@@ -87,7 +87,7 @@ lemma cpts_refl (h) (G) (L): reflexive … (cpts h G L 0).
 (* Advanced properties ******************************************************)
 
 lemma cpts_sort (h) (G) (L) (n):
-      ∀s. ⦃G,L⦄ ⊢ ⋆s ⬆*[h,n] ⋆((next h)^n s).
+      ∀s. ❪G,L❫ ⊢ ⋆s ⬆*[h,n] ⋆((next h)^n s).
 #h #G #L #n elim n -n [ // ]
 #n #IH #s <plus_SO_dx
 /3 width=3 by cpts_step_dx, cpt_sort/
@@ -96,14 +96,14 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 lemma cpts_inv_sort_sn (h) (n) (G) (L) (s):
-      ∀X2. ⦃G,L⦄ ⊢ ⋆s ⬆*[h,n] X2 → X2 = ⋆(((next h)^n) s).
+      ∀X2. ❪G,L❫ ⊢ ⋆s ⬆*[h,n] X2 → X2 = ⋆(((next h)^n) s).
 #h #n #G #L #s #X2 #H @(cpts_ind_dx … H) -X2 //
 #n1 #n2 #X #X2 #_ #IH #HX2 destruct
 elim (cpt_inv_sort_sn … HX2) -HX2 #H #_ destruct //
 qed-.
 
 lemma cpts_inv_lref_sn_ctop (h) (n) (G) (i):
-      ∀X2. ⦃G,⋆⦄ ⊢ #i ⬆*[h,n] X2 → ∧∧ X2 = #i & n = 0.
+      ∀X2. ❪G,⋆❫ ⊢ #i ⬆*[h,n] X2 → ∧∧ X2 = #i & n = 0.
 #h #n #G #i #X2 #H @(cpts_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -113,7 +113,7 @@ lemma cpts_inv_lref_sn_ctop (h) (n) (G) (i):
 qed-.
 
 lemma cpts_inv_zero_sn_unit (h) (n) (I) (K) (G):
-      ∀X2. ⦃G,K.ⓤ{I}⦄ ⊢ #0 ⬆*[h,n] X2 → ∧∧ X2 = #0 & n = 0.
+      ∀X2. ❪G,K.ⓤ[I]❫ ⊢ #0 ⬆*[h,n] X2 → ∧∧ X2 = #0 & n = 0.
 #h #n #I #G #K #X2 #H @(cpts_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -123,7 +123,7 @@ lemma cpts_inv_zero_sn_unit (h) (n) (I) (K) (G):
 qed-.
 
 lemma cpts_inv_gref_sn (h) (n) (G) (L) (l):
-      ∀X2. ⦃G,L⦄ ⊢ §l ⬆*[h,n] X2 → ∧∧ X2 = §l & n = 0.
+      ∀X2. ❪G,L❫ ⊢ §l ⬆*[h,n] X2 → ∧∧ X2 = §l & n = 0.
 #h #n #G #L #l #X2 #H @(cpts_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -133,9 +133,9 @@ lemma cpts_inv_gref_sn (h) (n) (G) (L) (l):
 qed-.
 
 lemma cpts_inv_cast_sn (h) (n) (G) (L) (U1) (T1):
-      ∀X2. ⦃G,L⦄ ⊢ ⓝU1.T1 ⬆*[h,n] X2 →
-      ∨∨ ∃∃U2,T2. ⦃G,L⦄ ⊢ U1 ⬆*[h,n] U2 & ⦃G,L⦄ ⊢ T1 ⬆*[h,n] T2 & X2 = ⓝU2.T2
-       | ∃∃m. ⦃G,L⦄ ⊢ U1 ⬆*[h,m] X2 & n = ↑m.
+      ∀X2. ❪G,L❫ ⊢ ⓝU1.T1 ⬆*[h,n] X2 →
+      ∨∨ ∃∃U2,T2. ❪G,L❫ ⊢ U1 ⬆*[h,n] U2 & ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 & X2 = ⓝU2.T2
+       | ∃∃m. ❪G,L❫ ⊢ U1 ⬆*[h,m] X2 & n = ↑m.
 #h #n #G #L #U1 #T1 #X2 #H @(cpts_ind_dx … H) -n -X2
 [ /3 width=5 by or_introl, ex3_2_intro/
 | #n1 #n2 #X #X2 #_ * *