update in ground_2, static_2, basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
index 7f617b13aa267e0ceef7cb942c0af034d78bc723..7f472e2ad1d4f0adda0847421e51569bbc0c2a11 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma
@@ -21,7 +21,7 @@ include "basic_2/rt_computation/cpxs.ma".
 (* Advanced properties ******************************************************)
 
 lemma cpxs_delta: ∀h,I,G,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
-                  ∀W2. ⇧*[1] V2 ≘ W2 → ❪G,K.ⓑ[I]V1❫ ⊢ #0 ⬈*[h] W2.
+                  ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓑ[I]V1❫ ⊢ #0 ⬈*[h] W2.
 #h #I #G #K #V1 #V2 #H @(cpxs_ind … H) -V2
 [ /3 width=3 by cpx_cpxs, cpx_delta/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
@@ -31,7 +31,7 @@ lemma cpxs_delta: ∀h,I,G,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
 qed.
 
 lemma cpxs_lref: ∀h,I,G,K,T,i. ❪G,K❫ ⊢ #i ⬈*[h] T →
-                 ∀U. ⇧*[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬈*[h] U.
+                 ∀U. ⇧[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬈*[h] U.
 #h #I #G #K #T #i #H @(cpxs_ind … H) -T
 [ /3 width=3 by cpx_cpxs, cpx_lref/
 | #T0 #T #_ #HT2 #IH #U #HTU
@@ -42,8 +42,8 @@ qed.
 
 (* Basic_2A1: was: cpxs_delta *)
 lemma cpxs_delta_drops: ∀h,I,G,L,K,V1,V2,i.
-                        ⇩*[i] L ≘ K.ⓑ[I]V1 → ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
-                        ∀W2. ⇧*[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈*[h] W2.
+                        ⇩[i] L ≘ K.ⓑ[I]V1 → ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
+                        ∀W2. ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈*[h] W2.
 #h #I #G #L #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
 [ /3 width=7 by cpx_cpxs, cpx_delta_drops/
 | #V #V2 #_ #HV2 #IH #W2 #HVW2
@@ -56,7 +56,7 @@ qed.
 
 lemma cpxs_inv_zero1: ∀h,G,L,T2. ❪G,L❫ ⊢ #0 ⬈*[h] T2 →
                       T2 = #0 ∨
-                      ∃∃I,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 & ⇧*[1] V2 ≘ T2 &
+                      ∃∃I,K,V1,V2. ❪G,K❫ ⊢ V1 ⬈*[h] V2 & ⇧[1] V2 ≘ T2 &
                                    L = K.ⓑ[I]V1.
 #h #G #L #T2 #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
@@ -71,7 +71,7 @@ qed-.
 
 lemma cpxs_inv_lref1: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #↑i ⬈*[h] T2 →
                       T2 = #(↑i) ∨
-                      ∃∃I,K,T. ❪G,K❫ ⊢ #i ⬈*[h] T & ⇧*[1] T ≘ T2 & L = K.ⓘ[I].
+                      ∃∃I,K,T. ❪G,K❫ ⊢ #i ⬈*[h] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
 #h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
@@ -86,8 +86,8 @@ qed-.
 (* Basic_2A1: was: cpxs_inv_lref1 *)
 lemma cpxs_inv_lref1_drops: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #i ⬈*[h] T2 →
                             T2 = #i ∨
-                            ∃∃I,K,V1,T1. ⇩*[i] L ≘ K.ⓑ[I]V1 & ❪G,K❫ ⊢ V1 ⬈*[h] T1 &
-                                         ⇧*[↑i] T1 ≘ T2.
+                            ∃∃I,K,V1,T1. ⇩[i] L ≘ K.ⓑ[I]V1 & ❪G,K❫ ⊢ V1 ⬈*[h] T1 &
+                                         ⇧[↑i] T1 ≘ T2.
 #h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct