update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
index 081eece9b1257698327268c01aa216e38beeafc5..64215875127b70271ae305ae841247cabf71aba2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
@@ -35,15 +35,15 @@ interpretation
 
 lemma cpms_ind_sn (h) (G) (L) (T2) (Q:relation2 …):
                   Q 0 T2 →
-                  (â\88\80n1,n2,T1,T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[n1,h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T ➡*[n2,h] T2 → Q n2 T → Q (n1+n2) T1) →
-                  â\88\80n,T1. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2 → Q n T1.
+                  (â\88\80n1,n2,T1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[n1,h] T â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡*[n2,h] T2 → Q n2 T → Q (n1+n2) T1) →
+                  â\88\80n,T1. â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2 → Q n T1.
 #h #G #L #T2 #Q @ltc_ind_sn_refl //
 qed-.
 
 lemma cpms_ind_dx (h) (G) (L) (T1) (Q:relation2 …):
                   Q 0 T1 →
-                  (â\88\80n1,n2,T,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n1,h] T â\86\92 Q n1 T â\86\92 â¦\83G,Lâ¦\84 ⊢ T ➡[n2,h] T2 → Q (n1+n2) T2) →
-                  â\88\80n,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2 → Q n T2.
+                  (â\88\80n1,n2,T,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n1,h] T â\86\92 Q n1 T â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡[n2,h] T2 → Q (n1+n2) T2) →
+                  â\88\80n,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2 → Q n T2.
 #h #G #L #T1 #Q @ltc_ind_dx_refl //
 qed-.
 
@@ -52,36 +52,36 @@ qed-.
 (* Basic_1: includes: pr1_pr0 *)
 (* Basic_1: uses: pr3_pr2 *)
 (* Basic_2A1: includes: cpr_cprs *)
-lemma cpm_cpms (h) (G) (L): â\88\80n,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2.
+lemma cpm_cpms (h) (G) (L): â\88\80n,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[n,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2.
 /2 width=1 by ltc_rc/ qed.
 
-lemma cpms_step_sn (h) (G) (L): â\88\80n1,T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n1,h] T →
-                                â\88\80n2,T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n2,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n1+n2,h] T2.
+lemma cpms_step_sn (h) (G) (L): â\88\80n1,T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡[n1,h] T →
+                                â\88\80n2,T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n2,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n1+n2,h] T2.
 /2 width=3 by ltc_sn/ qed-.
 
-lemma cpms_step_dx (h) (G) (L): â\88\80n1,T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n1,h] T →
-                                â\88\80n2,T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[n2,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n1+n2,h] T2.
+lemma cpms_step_dx (h) (G) (L): â\88\80n1,T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[n1,h] T →
+                                â\88\80n2,T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[n2,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n1+n2,h] T2.
 /2 width=3 by ltc_dx/ qed-.
 
 (* Basic_2A1: uses: cprs_bind_dx *)
 lemma cpms_bind_dx (n) (h) (G) (L):
-                   â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V2 →
-                   â\88\80I,T1,T2. â¦\83G,L.â\93\91{I}V1â¦\84 ⊢ T1 ➡*[n,h] T2 →
-                   â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 â\9e¡*[n,h] â\93\91{p,I}V2.T2.
+                   â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+                   â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡*[n,h] T2 →
+                   â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[n,h] â\93\91[p,I]V2.T2.
 #n #h #G #L #V1 #V2 #HV12 #I #T1 #T2 #H #a @(cpms_ind_sn … H) -T1
 /3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind/ qed.
 
 lemma cpms_appl_dx (n) (h) (G) (L):
-                   â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V2 →
-                   â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2 →
-                   â¦\83G,Lâ¦\84 ⊢ ⓐV1.T1 ➡*[n,h] ⓐV2.T2.
+                   â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+                   â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2 →
+                   â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ➡*[n,h] ⓐV2.T2.
 #n #h #G #L #V1 #V2 #HV12 #T1 #T2 #H @(cpms_ind_sn … H) -T1
 /3 width=3 by cpms_step_sn, cpm_cpms, cpm_appl/
 qed.
 
 lemma cpms_zeta (n) (h) (G) (L):
                 ∀T1,T. ⇧*[1] T ≘ T1 →
-                â\88\80V,T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ +ⓓV.T1 ➡*[n,h] T2.
+                â\88\80V,T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ +ⓓV.T1 ➡*[n,h] T2.
 #n #h #G #L #T1 #T #HT1 #V #T2 #H @(cpms_ind_dx … H) -T2
 /3 width=3 by cpms_step_dx, cpm_cpms, cpm_zeta/
 qed.
@@ -89,22 +89,22 @@ qed.
 (* Basic_2A1: uses: cprs_zeta *)
 lemma cpms_zeta_dx (n) (h) (G) (L):
                    ∀T2,T. ⇧*[1] T2 ≘ T →
-                   â\88\80V,T1. â¦\83G,L.â\93\93Vâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ +ⓓV.T1 ➡*[n,h] T2.
+                   â\88\80V,T1. â\9dªG,L.â\93\93Vâ\9d« â\8a¢ T1 â\9e¡*[n,h] T â\86\92 â\9dªG,Lâ\9d« ⊢ +ⓓV.T1 ➡*[n,h] T2.
 #n #h #G #L #T2 #T #HT2 #V #T1 #H @(cpms_ind_sn … H) -T1
 /3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind, cpm_zeta/
 qed.
 
 (* Basic_2A1: uses: cprs_eps *)
 lemma cpms_eps (n) (h) (G) (L):
-               â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2 →
-               â\88\80V. â¦\83G,Lâ¦\84 ⊢ ⓝV.T1 ➡*[n,h] T2.
+               â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2 →
+               â\88\80V. â\9dªG,Lâ\9d« ⊢ ⓝV.T1 ➡*[n,h] T2.
 #n #h #G #L #T1 #T2 #H @(cpms_ind_sn … H) -T1
 /3 width=3 by cpms_step_sn, cpm_cpms, cpm_eps/
 qed.
 
 lemma cpms_ee (n) (h) (G) (L):
-              â\88\80U1,U2. â¦\83G,Lâ¦\84 ⊢ U1 ➡*[n,h] U2 →
-              â\88\80T. â¦\83G,Lâ¦\84 ⊢ ⓝU1.T ➡*[↑n,h] U2.
+              â\88\80U1,U2. â\9dªG,Lâ\9d« ⊢ U1 ➡*[n,h] U2 →
+              â\88\80T. â\9dªG,Lâ\9d« ⊢ ⓝU1.T ➡*[↑n,h] U2.
 #n #h #G #L #U1 #U2 #H @(cpms_ind_sn … H) -U1 -n
 [ /3 width=1 by cpm_cpms, cpm_ee/
 | #n1 #n2 #U1 #U #HU1 #HU2 #_ #T >plus_S1
@@ -114,21 +114,21 @@ qed.
 
 (* Basic_2A1: uses: cprs_beta_dx *)
 lemma cpms_beta_dx (n) (h) (G) (L):
-                   â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V2 →
-                   â\88\80W1,W2. â¦\83G,Lâ¦\84 ⊢ W1 ➡[h] W2 →
-                   â\88\80T1,T2. â¦\83G,L.â\93\9bW1â¦\84 ⊢ T1 ➡*[n,h] T2 →
-                   â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{p}W1.T1 â\9e¡*[n,h] â\93\93{p}ⓝW2.V2.T2.
+                   â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+                   â\88\80W1,W2. â\9dªG,Lâ\9d« ⊢ W1 ➡[h] W2 →
+                   â\88\80T1,T2. â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡*[n,h] T2 →
+                   â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\9b[p]W1.T1 â\9e¡*[n,h] â\93\93[p]ⓝW2.V2.T2.
 #n #h #G #L #V1 #V2 #HV12 #W1 #W2 #HW12 #T1 #T2 #H @(cpms_ind_dx … H) -T2
 /4 width=7 by cpms_step_dx, cpm_cpms, cpms_bind_dx, cpms_appl_dx, cpm_beta/
 qed.
 
 (* Basic_2A1: uses: cprs_theta_dx *)
 lemma cpms_theta_dx (n) (h) (G) (L):
-                    â\88\80V1,V. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V →
+                    â\88\80V1,V. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V →
                     ∀V2. ⇧*[1] V ≘ V2 →
-                    â\88\80W1,W2. â¦\83G,Lâ¦\84 ⊢ W1 ➡[h] W2 →
-                    â\88\80T1,T2. â¦\83G,L.â\93\93W1â¦\84 ⊢ T1 ➡*[n,h] T2 →
-                    â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{p}W1.T1 â\9e¡*[n,h] â\93\93{p}W2.ⓐV2.T2.
+                    â\88\80W1,W2. â\9dªG,Lâ\9d« ⊢ W1 ➡[h] W2 →
+                    â\88\80T1,T2. â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡*[n,h] T2 →
+                    â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\93[p]W1.T1 â\9e¡*[n,h] â\93\93[p]W2.ⓐV2.T2.
 #n #h #G #L #V1 #V #HV1 #V2 #HV2 #W1 #W2 #HW12 #T1 #T2 #H @(cpms_ind_dx … H) -T2
 /4 width=9 by cpms_step_dx, cpm_cpms, cpms_bind_dx, cpms_appl_dx, cpm_theta/
 qed.
@@ -142,7 +142,7 @@ lemma cprs_refl: ∀h,G,L. reflexive … (cpms h G L 0).
 (* Advanced properties ******************************************************)
 
 lemma cpms_sort (h) (G) (L) (n):
-                â\88\80s. â¦\83G,Lâ¦\84 ⊢ ⋆s ➡*[n,h] ⋆((next h)^n s).
+                â\88\80s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡*[n,h] ⋆((next h)^n s).
 #h #G #L #n elim n -n [ // ]
 #n #IH #s <plus_SO_dx
 /3 width=3 by cpms_step_dx, cpm_sort/
@@ -150,14 +150,14 @@ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cpms_inv_sort1 (n) (h) (G) (L): â\88\80X2,s. â¦\83G,Lâ¦\84 ⊢ ⋆s ➡*[n,h] X2 → X2 = ⋆(((next h)^n) s).
+lemma cpms_inv_sort1 (n) (h) (G) (L): â\88\80X2,s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡*[n,h] X2 → X2 = ⋆(((next h)^n) s).
 #n #h #G #L #X2 #s #H @(cpms_ind_dx … H) -X2 //
 #n1 #n2 #X #X2 #_ #IH #HX2 destruct
 elim (cpm_inv_sort1 … HX2) -HX2 #H #_ destruct //
 qed-.
 
 lemma cpms_inv_lref1_ctop (n) (h) (G):
-      â\88\80X2,i. â¦\83G,â\8b\86â¦\84 ⊢ #i ➡*[n,h] X2 → ∧∧ X2 = #i & n = 0.
+      â\88\80X2,i. â\9dªG,â\8b\86â\9d« ⊢ #i ➡*[n,h] X2 → ∧∧ X2 = #i & n = 0.
 #n #h #G #X2 #i #H @(cpms_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -167,7 +167,7 @@ lemma cpms_inv_lref1_ctop (n) (h) (G):
 qed-.
 
 lemma cpms_inv_zero1_unit (n) (h) (I) (K) (G):
-      â\88\80X2. â¦\83G,K.â\93¤{I}â¦\84 ⊢ #0 ➡*[n,h] X2 → ∧∧ X2 = #0 & n = 0.
+      â\88\80X2. â\9dªG,K.â\93¤[I]â\9d« ⊢ #0 ➡*[n,h] X2 → ∧∧ X2 = #0 & n = 0.
 #n #h #I #G #K #X2 #H @(cpms_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -177,7 +177,7 @@ lemma cpms_inv_zero1_unit (n) (h) (I) (K) (G):
 qed-.
 
 lemma cpms_inv_gref1 (n) (h) (G) (L):
-      â\88\80X2,l. â¦\83G,Lâ¦\84 ⊢ §l ➡*[n,h] X2 → ∧∧ X2 = §l & n = 0.
+      â\88\80X2,l. â\9dªG,Lâ\9d« ⊢ §l ➡*[n,h] X2 → ∧∧ X2 = §l & n = 0.
 #n #h #G #L #X2 #l #H @(cpms_ind_dx … H) -X2
 [ /2 width=1 by conj/
 | #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
@@ -187,10 +187,10 @@ lemma cpms_inv_gref1 (n) (h) (G) (L):
 qed-.
 
 lemma cpms_inv_cast1 (h) (n) (G) (L):
-      â\88\80W1,T1,X2. â¦\83G,Lâ¦\84 ⊢ ⓝW1.T1 ➡*[n,h] X2 →
-      â\88¨â\88¨ â\88\83â\88\83W2,T2. â¦\83G,Lâ¦\84 â\8a¢ W1 â\9e¡*[n,h] W2 & â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2 & X2 = ⓝW2.T2
-       | â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] X2
-       | â\88\83â\88\83m. â¦\83G,Lâ¦\84 ⊢ W1 ➡*[m,h] X2 & n = ↑m.
+      â\88\80W1,T1,X2. â\9dªG,Lâ\9d« ⊢ ⓝW1.T1 ➡*[n,h] X2 →
+      â\88¨â\88¨ â\88\83â\88\83W2,T2. â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡*[n,h] W2 & â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2 & X2 = ⓝW2.T2
+       | â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] X2
+       | â\88\83â\88\83m. â\9dªG,Lâ\9d« ⊢ W1 ➡*[m,h] X2 & n = ↑m.
 #h #n #G #L #W1 #T1 #X2 #H @(cpms_ind_dx … H) -n -X2
 [ /3 width=5 by or3_intro0, ex3_2_intro/
 | #n1 #n2 #X #X2 #_ * [ * || * ]