partial commit: "computation" component ...

[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 4b19e3db2c781d967c7eb39bd435643ec8a05a22..1eee44b51e8a7ff1c3d637a8c39908db12e4f1c8 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
@@ -22,9 +22,9 @@ 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⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ →
+lemma csn_applv_cnx: ∀h,g,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 *)
+#h #g #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
 @csn_appl_simple_tstc // -HV /2 width=1/ -IHV -HVs
@@ -33,8 +33,8 @@ lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
 elim (H0) -H0 //
 qed.
 
-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)
+lemma csn_applv_sort: ∀h,g,G,L,k,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Vs → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.⋆k.
+#h #g #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
 #Hkl #Vs elim Vs -Vs /2 width=1/
@@ -49,9 +49,9 @@ 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. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.ⓓ{a}ⓝW.V.T →
+lemma csn_applv_beta: ∀h,g,a,G,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/
+#h #g #a #G #L #Vs elim Vs -Vs /2 width=1/
 #V0 #Vs #IHV #V #W #T #H1T
 lapply (csn_fwd_pair_sn … H1T) #HV0
 lapply (csn_fwd_flat_dx … H1T) #H2T
@@ -63,10 +63,10 @@ elim (cpxs_fwd_beta_vector … H) -H #H
 ]
 qed.
 
-lemma csn_applv_delta: ∀h,g,I,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
+lemma csn_applv_delta: ∀h,g,I,G,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
                        ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
                        ∀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 #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
 [ #H
   lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
   lapply (csn_inv_lift … H … HLK0 HV12) -V2 -HLK0 /2 width=5/
@@ -83,10 +83,10 @@ lemma csn_applv_delta: ∀h,g,I,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
 qed.
 
 (* Basic_1: was just: sn3_appls_abbr *)
-lemma csn_applv_theta: ∀h,g,a,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+lemma csn_applv_theta: ∀h,g,a,G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
                        ∀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/
+#h #g #a #G #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
 elim H -V1s -V2s /2 width=3/
@@ -102,9 +102,9 @@ 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. ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.W → ⦃G, L⦄ ⊢ ⬊*[h, g] ⒶVs.T →
+lemma csn_applv_cast: ∀h,g,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/
+#h #g #G #L #Vs elim Vs -Vs /2 width=1/
 #V #Vs #IHV #W #T #H1W #H1T
 lapply (csn_fwd_pair_sn … H1W) #HV
 lapply (csn_fwd_flat_dx … H1W) #H2W
@@ -118,12 +118,12 @@ elim (cpxs_fwd_cast_vector … H) -H #H
 ]
 qed.
 
-theorem csn_acr: ∀h,g. acr (cpx h g) (eq …) (csn h g) (λL,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T).
+theorem csn_acr: ∀h,g. acr (cpx h g) (eq …) (csn h g) (λG,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T).
 #h #g @mk_acr //
 [ /3 width=1/
 |2,3,6: /2 width=1/
 | /2 width=7/
-| #L #V1s #V2s #HV12s #a #V #T #H #HV
+| #G #L #V1s #V2s #HV12s #a #V #T #H #HV
   @(csn_applv_theta … HV12s) -HV12s
   @(csn_abbr) //
 | @csn_lift