partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / csn_tstc_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_tstc_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_tstc_vector.ma
index 1237049790a17766af0cee6b19fd6652189f74cf..4b19e3db2c781d967c7eb39bd435643ec8a05a22 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_tstc_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_tstc_vector.ma
@@ -22,8 +22,8 @@ include "basic_2/computation/csn_vector.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_1: was just: sn3_appls_lref *)
-lemma csn_applv_cnx: ∀h,g,L,T. 𝐒⦃T⦄ → ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ →
-                     ∀Vs. ⦃h, L⦄ ⊢ ⬊*[g] Vs → ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.T.
+lemma csn_applv_cnx: ∀h,g,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ →
+                     ∀Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T.
 #h #g #L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(cnx_csn … H2T) ] (**) (* /2 width=1/ does not work *)
 #V #Vs #IHV #H
 elim (csnv_inv_cons … H) -H #HV #HVs
@@ -33,7 +33,7 @@ lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
 elim (H0) -H0 //
 qed.
 
-lemma csn_applv_sort: ∀h,g,L,k,Vs. ⦃h, L⦄ ⊢ ⬊*[g] Vs → ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.⋆k.
+lemma csn_applv_sort: ∀h,g,L,k,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.⋆k.
 #h #g #L #k elim (deg_total h g k)
 #l generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=1/ ]
 #l #IHl #k #Hkl lapply (deg_next_SO … Hkl) -Hkl
@@ -49,8 +49,8 @@ elim (cpxs_fwd_sort_vector … H) -H #H
 qed.
 
 (* Basic_1: was just: sn3_appls_beta *)
-lemma csn_applv_beta: ∀h,g,a,L,Vs,V,W,T. ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.ⓓ{a}ⓝW.V.T →
-                      ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs. ⓐV.ⓛ{a}W.T.
+lemma csn_applv_beta: ∀h,g,a,L,Vs,V,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓓ{a}ⓝW.V.T →
+                      ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs. ⓐV.ⓛ{a}W.T.
 #h #g #a #L #Vs elim Vs -Vs /2 width=1/
 #V0 #Vs #IHV #V #W #T #H1T
 lapply (csn_fwd_pair_sn … H1T) #HV0
@@ -65,7 +65,7 @@ qed.
 
 lemma csn_applv_delta: ∀h,g,I,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
                        ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
-                       ∀Vs. ⦃h, L⦄ ⊢ ⬊*[g] (ⒶVs.V2) → ⦃h, L⦄ ⊢ ⬊*[g] (ⒶVs.#i).
+                       ∀Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] (ⒶVs.V2) → ⦃G, L⦄ ⊢ ⬊*[h, g] (ⒶVs.#i).
 #h #g #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
 [ #H
   lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
@@ -84,8 +84,8 @@ qed.
 
 (* Basic_1: was just: sn3_appls_abbr *)
 lemma csn_applv_theta: ∀h,g,a,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                       ∀V,T. ⦃h, L⦄ ⊢ ⬊*[g] ⓓ{a}V.ⒶV2s.T →
-                       ⦃h, L⦄ ⊢ ⬊*[g] ⒶV1s.ⓓ{a}V.T.
+                       ∀V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓓ{a}V.ⒶV2s.T →
+                       ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶV1s.ⓓ{a}V.T.
 #h #g #a #L #V1s #V2s * -V1s -V2s /2 width=1/
 #V1s #V2s #V1 #V2 #HV12 #H
 generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
@@ -102,8 +102,8 @@ elim (cpxs_fwd_theta_vector … (V2@V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
 qed.
 
 (* Basic_1: was just: sn3_appls_cast *)
-lemma csn_applv_cast: ∀h,g,L,Vs,W,T. ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.W → ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.T →
-                      ⦃h, L⦄ ⊢ ⬊*[g] ⒶVs.ⓝW.T.
+lemma csn_applv_cast: ∀h,g,L,Vs,W,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.W → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T →
+                      ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓝW.T.
 #h #g #L #Vs elim Vs -Vs /2 width=1/
 #V #Vs #IHV #W #T #H1W #H1T
 lapply (csn_fwd_pair_sn … H1W) #HV
@@ -118,7 +118,7 @@ elim (cpxs_fwd_cast_vector … H) -H #H
 ]
 qed.
 
-theorem csn_acr: ∀h,g. acr (cpx h g) (eq …) (csn h g) (λL,T. ⦃h, L⦄ ⊢ ⬊*[g] T).
+theorem csn_acr: ∀h,g. acr (cpx h g) (eq …) (csn h g) (λL,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T).
 #h #g @mk_acr //
 [ /3 width=1/
 |2,3,6: /2 width=1/