update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma
index f98626953f8dbe51980fc44de7c85f953a53fa79..894ece04c1f3e937f03201044a5465133b84d33c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma
@@ -46,40 +46,40 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma cpms_delta (n) (h) (G): â\88\80K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ➡*[n,h] V2 →
-                              â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â¦\83G,K.â\93\93V1â¦\84 ⊢ #0 ➡*[n,h] W2.
+lemma cpms_delta (n) (h) (G): â\88\80K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡*[n,h] V2 →
+                              â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\93V1â\9d« ⊢ #0 ➡*[n,h] W2.
 #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2
 [ /3 width=3 by cpm_cpms, cpm_delta/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
-  elim (lifts_total V (ð\9d\90\94â\9d´1â\9dµ)) #W #HVW
+  elim (lifts_total V (ð\9d\90\94â\9d¨1â\9d©)) #W #HVW
   /5 width=11 by cpms_step_dx, cpm_lifts_bi, drops_refl, drops_drop/
 ]
 qed.
 
-lemma cpms_ell (n) (h) (G): â\88\80K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ➡*[n,h] V2 →
-                            â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â¦\83G,K.â\93\9bV1â¦\84 ⊢ #0 ➡*[↑n,h] W2.
+lemma cpms_ell (n) (h) (G): â\88\80K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡*[n,h] V2 →
+                            â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\9bV1â\9d« ⊢ #0 ➡*[↑n,h] W2.
 #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2
 [ /3 width=3 by cpm_cpms, cpm_ell/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
-  elim (lifts_total V (ð\9d\90\94â\9d´1â\9dµ)) #W #HVW >plus_S1
+  elim (lifts_total V (ð\9d\90\94â\9d¨1â\9d©)) #W #HVW >plus_S1
   /5 width=11 by cpms_step_dx, cpm_lifts_bi, drops_refl, drops_drop/
 ]
 qed.
 
-lemma cpms_lref (n) (h) (I) (G): â\88\80K,T,i. â¦\83G,Kâ¦\84 ⊢ #i ➡*[n,h] T →
-                                 â\88\80U. â\87§*[1] T â\89\98 U â\86\92 â¦\83G,K.â\93\98{I}â¦\84 ⊢ #↑i ➡*[n,h] U.
+lemma cpms_lref (n) (h) (I) (G): â\88\80K,T,i. â\9dªG,Kâ\9d« ⊢ #i ➡*[n,h] T →
+                                 â\88\80U. â\87§*[1] T â\89\98 U â\86\92 â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ➡*[n,h] U.
 #n #h #I #G #K #T #i #H @(cpms_ind_dx … H) -T
 [ /3 width=3 by cpm_cpms, cpm_lref/
 | #n1 #n2 #T #T2 #_ #IH #HT2 #U2 #HTU2
-  elim (lifts_total T (ð\9d\90\94â\9d´1â\9dµ)) #U #TU
+  elim (lifts_total T (ð\9d\90\94â\9d¨1â\9d©)) #U #TU
   /5 width=11 by cpms_step_dx, cpm_lifts_bi, drops_refl, drops_drop/
 ]
 qed.
 
 lemma cpms_cast_sn (n) (h) (G) (L):
-                   â\88\80U1,U2. â¦\83G,Lâ¦\84 ⊢ U1 ➡*[n,h] U2 →
-                   â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 →
-                   â¦\83G,Lâ¦\84 ⊢ ⓝU1.T1 ➡*[n,h] ⓝU2.T2.
+                   â\88\80U1,U2. â\9dªG,Lâ\9d« ⊢ U1 ➡*[n,h] U2 →
+                   â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] T2 →
+                   â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ➡*[n,h] ⓝU2.T2.
 #n #h #G #L #U1 #U2 #H @(cpms_ind_sn … H) -U1 -n
 [ /3 width=3 by cpm_cpms, cpm_cast/
 | #n1 #n2 #U1 #U #HU1 #_ #IH #T1 #T2 #H
@@ -92,26 +92,26 @@ qed.
 (* Basic_2A1: uses: cprs_delta *)
 lemma cpms_delta_drops (n) (h) (G):
                        ∀L,K,V,i. ⇩*[i] L ≘ K.ⓓV →
-                       â\88\80V2. â¦\83G,Kâ¦\84 ⊢ V ➡*[n,h] V2 →
-                       â\88\80W2. â\87§*[â\86\91i] V2 â\89\98 W2 â\86\92 â¦\83G,Lâ¦\84 ⊢ #i ➡*[n,h] W2.
+                       â\88\80V2. â\9dªG,Kâ\9d« ⊢ V ➡*[n,h] V2 →
+                       â\88\80W2. â\87§*[â\86\91i] V2 â\89\98 W2 â\86\92 â\9dªG,Lâ\9d« ⊢ #i ➡*[n,h] W2.
 #n #h #G #L #K #V #i #HLK #V2 #H @(cpms_ind_dx … H) -V2
 [ /3 width=6 by cpm_cpms, cpm_delta_drops/
 | #n1 #n2 #V1 #V2 #_ #IH #HV12 #W2 #HVW2
   lapply (drops_isuni_fwd_drop2 … HLK) -HLK // #HLK
-  elim (lifts_total V1 (ð\9d\90\94â\9d´â\86\91iâ\9dµ)) #W1 #HVW1
+  elim (lifts_total V1 (ð\9d\90\94â\9d¨â\86\91iâ\9d©)) #W1 #HVW1
   /3 width=11 by cpm_lifts_bi, cpms_step_dx/
 ]
 qed.
 
 lemma cpms_ell_drops (n) (h) (G):
                      ∀L,K,W,i. ⇩*[i] L ≘ K.ⓛW →
-                     â\88\80W2. â¦\83G,Kâ¦\84 ⊢ W ➡*[n,h] W2 →
-                     â\88\80V2. â\87§*[â\86\91i] W2 â\89\98 V2 â\86\92 â¦\83G,Lâ¦\84 ⊢ #i ➡*[↑n,h] V2.
+                     â\88\80W2. â\9dªG,Kâ\9d« ⊢ W ➡*[n,h] W2 →
+                     â\88\80V2. â\87§*[â\86\91i] W2 â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« ⊢ #i ➡*[↑n,h] V2.
 #n #h #G #L #K #W #i #HLK #W2 #H @(cpms_ind_dx … H) -W2
 [ /3 width=6 by cpm_cpms, cpm_ell_drops/
 | #n1 #n2 #W1 #W2 #_ #IH #HW12 #V2 #HWV2
   lapply (drops_isuni_fwd_drop2 … HLK) -HLK // #HLK
-  elim (lifts_total W1 (ð\9d\90\94â\9d´â\86\91iâ\9dµ)) #V1 #HWV1 >plus_S1
+  elim (lifts_total W1 (ð\9d\90\94â\9d¨â\86\91iâ\9d©)) #V1 #HWV1 >plus_S1
   /3 width=11 by cpm_lifts_bi, cpms_step_dx/
 ]
 qed.
@@ -119,11 +119,11 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma cpms_inv_lref1_drops (n) (h) (G):
-                           â\88\80L,T2,i. â¦\83G,Lâ¦\84 ⊢ #i ➡*[n,h] T2 →
+                           â\88\80L,T2,i. â\9dªG,Lâ\9d« ⊢ #i ➡*[n,h] T2 →
                            ∨∨ ∧∧ T2 = #i & n = 0
-                            | â\88\83â\88\83K,V,V2. â\87©*[i] L â\89\98 K.â\93\93V & â¦\83G,Kâ¦\84 ⊢ V ➡*[n,h] V2 &
+                            | â\88\83â\88\83K,V,V2. â\87©*[i] L â\89\98 K.â\93\93V & â\9dªG,Kâ\9d« ⊢ V ➡*[n,h] V2 &
                                         ⇧*[↑i] V2 ≘ T2
-                            | â\88\83â\88\83m,K,V,V2. â\87©*[i] L â\89\98 K.â\93\9bV & â¦\83G,Kâ¦\84 ⊢ V ➡*[m,h] V2 &
+                            | â\88\83â\88\83m,K,V,V2. â\87©*[i] L â\89\98 K.â\93\9bV & â\9dªG,Kâ\9d« ⊢ V ➡*[m,h] V2 &
                                           ⇧*[↑i] V2 ≘ T2 & n = ↑m.
 #n #h #G #L #T2 #i #H @(cpms_ind_dx … H) -T2
 [ /3 width=1 by or3_intro0, conj/
@@ -147,9 +147,9 @@ lemma cpms_inv_lref1_drops (n) (h) (G):
 qed-.
 
 lemma cpms_inv_delta_sn (n) (h) (G) (K) (V):
-      â\88\80T2. â¦\83G,K.â\93\93Vâ¦\84 ⊢ #0 ➡*[n,h] T2 →
+      â\88\80T2. â\9dªG,K.â\93\93Vâ\9d« ⊢ #0 ➡*[n,h] T2 →
       ∨∨ ∧∧ T2 = #0 & n = 0
-       | â\88\83â\88\83V2. â¦\83G,Kâ¦\84 ⊢ V ➡*[n,h] V2 & ⇧*[1] V2 ≘ T2.
+       | â\88\83â\88\83V2. â\9dªG,Kâ\9d« ⊢ V ➡*[n,h] V2 & ⇧*[1] V2 ≘ T2.
 #n #h #G #K #V #T2 #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -162,9 +162,9 @@ elim (cpms_inv_lref1_drops … H) -H *
 qed-.
 
 lemma cpms_inv_ell_sn (n) (h) (G) (K) (V):
-      â\88\80T2. â¦\83G,K.â\93\9bVâ¦\84 ⊢ #0 ➡*[n,h] T2 →
+      â\88\80T2. â\9dªG,K.â\93\9bVâ\9d« ⊢ #0 ➡*[n,h] T2 →
       ∨∨ ∧∧ T2 = #0 & n = 0
-       | â\88\83â\88\83m,V2. â¦\83G,Kâ¦\84 ⊢ V ➡*[m,h] V2 & ⇧*[1] V2 ≘ T2 & n = ↑m.
+       | â\88\83â\88\83m,V2. â\9dªG,Kâ\9d« ⊢ V ➡*[m,h] V2 & ⇧*[1] V2 ≘ T2 & n = ↑m.
 #n #h #G #K #V #T2 #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -177,28 +177,28 @@ elim (cpms_inv_lref1_drops … H) -H *
 qed-.
 
 lemma cpms_inv_lref_sn (n) (h) (G) (I) (K):
-      â\88\80U2,i. â¦\83G,K.â\93\98{I}â¦\84 ⊢ #↑i ➡*[n,h] U2 →
+      â\88\80U2,i. â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ➡*[n,h] U2 →
       ∨∨ ∧∧ U2 = #↑i & n = 0
-       | â\88\83â\88\83T2. â¦\83G,Kâ¦\84 ⊢ #i ➡*[n,h] T2 & ⇧*[1] T2 ≘ U2.
+       | â\88\83â\88\83T2. â\9dªG,Kâ\9d« ⊢ #i ➡*[n,h] T2 & ⇧*[1] T2 ≘ U2.
 #n #h #G #I #K #U2 #i #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
 | #L #V #V2 #H #HV2 #HVU2
   lapply (drops_inv_drop1 … H) -H #HLK
-  elim (lifts_split_trans â\80¦ HVU2 (ð\9d\90\94â\9d´â\86\91iâ\9dµ) (ð\9d\90\94â\9d´1â\9dµ)) -HVU2
+  elim (lifts_split_trans â\80¦ HVU2 (ð\9d\90\94â\9d¨â\86\91iâ\9d©) (ð\9d\90\94â\9d¨1â\9d©)) -HVU2
   [| // ] #T2 #HVT2 #HTU2
   /4 width=6 by cpms_delta_drops, ex2_intro, or_intror/
 | #m #L #V #V2 #H #HV2 #HVU2 #H0 destruct
   lapply (drops_inv_drop1 … H) -H #HLK
-  elim (lifts_split_trans â\80¦ HVU2 (ð\9d\90\94â\9d´â\86\91iâ\9dµ) (ð\9d\90\94â\9d´1â\9dµ)) -HVU2
+  elim (lifts_split_trans â\80¦ HVU2 (ð\9d\90\94â\9d¨â\86\91iâ\9d©) (ð\9d\90\94â\9d¨1â\9d©)) -HVU2
   [| // ] #T2 #HVT2 #HTU2
   /4 width=6 by cpms_ell_drops, ex2_intro, or_intror/
 ]
 qed-.
 
 fact cpms_inv_succ_sn (n) (h) (G) (L):
-                      â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[↑n,h] T2 →
-                      â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[1,h] T & â¦\83G,Lâ¦\84 ⊢ T ➡*[n,h] T2.
+                      â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[↑n,h] T2 →
+                      â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[1,h] T & â\9dªG,Lâ\9d« ⊢ T ➡*[n,h] T2.
 #n #h #G #L #T1 #T2
 @(insert_eq_0 … (↑n)) #m #H
 @(cpms_ind_sn … H) -T1 -m