commit completed: now we support two versions of slicing for local

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
index e16b976a797067b40948fa927ab3837e8681f4d1..55099d3253c54be1b9354ce3b346b856d0c3d9ca 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_tstc_vector.ma
@@ -27,7 +27,7 @@ lemma csx_applv_cnx: ∀h,g,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T
 #h #g #G #L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(cnx_csx … H2T) ] (**) (* /2 width=1/ does not work *)
 #V #Vs #IHV #H
 elim (csxv_inv_cons … H) -H #HV #HVs
-@csx_appl_simple_tstc // -HV /2 width=1/ -IHV -HVs
+@csx_appl_simple_tstc /2 width=1 by applv_simple/ -IHV -HV -HVs
 #X #H #H0
 lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
 elim (H0) -H0 //
@@ -35,49 +35,47 @@ qed.
 
 lemma csx_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 generalize in match k; -k @(nat_ind_plus … l) -l [ /3 width=1 by csx_applv_cnx, cnx_sort, simple_atom/ ]
 #l #IHl #k #Hkl lapply (deg_next_SO … Hkl) -Hkl
-#Hkl #Vs elim Vs -Vs /2 width=1/
+#Hkl #Vs elim Vs -Vs /2 width=1 by/
 #V #Vs #IHVs #HVVs
 elim (csxv_inv_cons … HVVs) #HV #HVs
-@csx_appl_simple_tstc // -HV /2 width=1/ -IHVs -HVs
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_atom/ -IHVs -HV -HVs
 #X #H #H0
 elim (cpxs_fwd_sort_vector … H) -H #H
 [ elim H0 -H0 //
-| -H0 @(csx_cpxs_trans … (Ⓐ(V@Vs).⋆(next h k))) /2 width=1/
+| -H0 @(csx_cpxs_trans … (Ⓐ(V@Vs).⋆(next h k))) /2 width=1 by cpxs_flat_dx/
 ]
 qed.
 
 (* Basic_1: was just: sn3_appls_beta *)
 lemma csx_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 #G #L #Vs elim Vs -Vs /2 width=1/
+#h #g #a #G #L #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
 #V0 #Vs #IHV #V #W #T #H1T
 lapply (csx_fwd_pair_sn … H1T) #HV0
 lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_tstc // -HV0 /2 width=1/ -IHV -H2T
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
 #X #H #H0
 elim (cpxs_fwd_beta_vector … H) -H #H
 [ -H1T elim H0 -H0 //
-| -H0 @(csx_cpxs_trans … H1T) -H1T /2 width=1/
+| -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
 ]
 qed.
 
-lemma csx_applv_delta: ∀h,g,I,G,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
+lemma csx_applv_delta: ∀h,g,I,G,L,K,V1,i. ⇩[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 #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
-[ #H
-  lapply (ldrop_fwd_drop2 … HLK) #HLK0
-  lapply (csx_inv_lift … H … HLK0 HV12) -V2 -HLK0 /2 width=5/
+[ /4 width=12 by csx_inv_lift, csx_lref_bind, ldrop_fwd_drop2/
 | #V #Vs #IHV #H1T
   lapply (csx_fwd_pair_sn … H1T) #HV
   lapply (csx_fwd_flat_dx … H1T) #H2T
-  @csx_appl_simple_tstc // -HV /2 width=1/ -IHV -H2T
+  @csx_appl_simple_tstc /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
   #X #H #H0
   elim (cpxs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
   [ -H1T elim H0 -H0 //
-  | -H0 @(csx_cpxs_trans … H1T) -H1T /2 width=1/
+  | -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
   ]
 ]
 qed.
@@ -86,46 +84,46 @@ qed.
 lemma csx_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 #G #L #V1s #V2s * -V1s -V2s /2 width=1/
+#h #g #a #G #L #V1s #V2s * -V1s -V2s /2 width=1 by/
 #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/
+elim H -V1s -V2s /2 width=3 by csx_appl_theta/
 #V1s #V2s #V1 #V2 #HV12 #HV12s #IHV12s #W1 #W2 #HW12 #V #T #H
 lapply (csx_appl_theta … HW12 … H) -H -HW12 #H
 lapply (csx_fwd_pair_sn … H) #HW1
 lapply (csx_fwd_flat_dx … H) #H1
-@csx_appl_simple_tstc // -HW1 /2 width=3/ -IHV12s -H1 #X #H1 #H2
-elim (cpxs_fwd_theta_vector … (V2@V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
+@csx_appl_simple_tstc /2 width=3 by simple_flat/ -IHV12s -HW1 -H1 #X #H1 #H2
+elim (cpxs_fwd_theta_vector … (V2@V2s) … H1) -H1 /2 width=1 by liftv_cons/ -HV12s -HV12
 [ -H #H elim H2 -H2 //
-| -H2 #H1 @(csx_cpxs_trans … H) -H /2 width=1/
+| -H2 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
 ]
 qed.
 
 (* Basic_1: was just: sn3_appls_cast *)
 lemma csx_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 #G #L #Vs elim Vs -Vs /2 width=1/
+#h #g #G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
 #V #Vs #IHV #W #T #H1W #H1T
 lapply (csx_fwd_pair_sn … H1W) #HV
 lapply (csx_fwd_flat_dx … H1W) #H2W
 lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_tstc // -HV /2 width=1/ -IHV -H2W -H2T
+@csx_appl_simple_tstc /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2W -H2T
 #X #H #H0
 elim (cpxs_fwd_cast_vector … H) -H #H
 [ -H1W -H1T elim H0 -H0 //
-| -H1W -H0 @(csx_cpxs_trans … H1T) -H1T /2 width=1/
-| -H1T -H0 @(csx_cpxs_trans … H1W) -H1W /2 width=1/
+| -H1W -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
+| -H1T -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
 ]
 qed.
 
 theorem csx_acr: ∀h,g. acr (cpx h g) (eq …) (csx 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/
+[ /3 width=1 by csx_applv_cnx/
+|2,3,6: /2 width=1 by csx_applv_beta, csx_applv_sort, csx_applv_cast/
+| /2 width=7 by csx_applv_delta/
 | #G #L #V1s #V2s #HV12s #a #V #T #H #HV
   @(csx_applv_theta … HV12s) -HV12s
-  @(csx_abbr) //
-| @csx_lift
+  @csx_abbr //
+| /2 width=8 by csx_lift/
 ]
 qed.