X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_tstc_vector.ma;h=becbd624d463d01b6c002d79b1029e13948299d7;hb=795ac6cc4ef54b4470b5e2fba287acca440c9c18;hp=55ea0dff906488550ef7529371e7d1b21f3d1e74;hpb=598a5c56535a8339f6533227ab580aff64e2d41c;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
index 55ea0dff9..becbd624d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc_vector.ma
@@ -22,36 +22,36 @@ include "basic_2/computation/cpxs_tstc.ma".
 
 (* Basic_1: was just: nf2_iso_appls_lref *)
 lemma cpxs_fwd_cnx_vector: ∀h,g,G,L,T.  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ →
-                           ∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.T ➡*[h, g] U → ⒶVs.T ≃ U.
+                           ∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.T ➡*[h, g] U → ⒶVs.T ≂ U.
 #h #g #G #L #T #H1T #H2T #Vs elim Vs -Vs [ @(cpxs_fwd_cnx … H2T) ] (**) (* /2 width=3 by cpxs_fwd_cnx/ does not work *)
 #V #Vs #IHVs #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair/
 | #a #W0 #T0 #HT0 #HU
   lapply (IHVs … HT0) -IHVs -HT0 #HT0
-  elim (tstc_inv_bind_appls_simple … HT0) //
+  elim (tstc_inv_bind_applv_simple … HT0) //
 | #a #V1 #V2 #V0 #T0 #HV1 #HV12 #HT0 #HU
   lapply (IHVs … HT0) -IHVs -HT0 #HT0
-  elim (tstc_inv_bind_appls_simple … HT0) //
+  elim (tstc_inv_bind_applv_simple … HT0) //
 ]
 qed-.
 
 lemma cpxs_fwd_sort_vector: ∀h,g,G,L,k,Vs,U. ⦃G, L⦄ ⊢ ⒶVs.⋆k ➡*[h, g] U →
-                            ⒶVs.⋆k ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.⋆(next h k) ➡*[h, g] U.
+                            ⒶVs.⋆k ≂ U ∨ ⦃G, L⦄ ⊢ ⒶVs.⋆(next h k) ➡*[h, g] U.
 #h #g #G #L #k #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_sort/
 #V #Vs #IHVs #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
 | #a #W1 #T1 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
-  [ elim (tstc_inv_bind_appls_simple … HT1) //
+  [ elim (tstc_inv_bind_applv_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV.ⓛ{a}W1.T1)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
   ]
 | #a #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
-  [ elim (tstc_inv_bind_appls_simple … HT1) //
+  [ elim (tstc_inv_bind_applv_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV1.ⓓ{a}V3.T1)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
@@ -62,21 +62,21 @@ qed-.
 
 (* Basic_1: was just: pr3_iso_appls_beta *)
 lemma cpxs_fwd_beta_vector: ∀h,g,a,G,L,Vs,V,W,T,U. ⦃G, L⦄ ⊢ ⒶVs.ⓐV.ⓛ{a}W.T ➡*[h, g] U →
-                            ⒶVs. ⓐV. ⓛ{a}W. T ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.ⓓ{a}ⓝW.V.T ➡*[h, g] U.
+                            ⒶVs. ⓐV. ⓛ{a}W. T ≂ U ∨ ⦃G, L⦄ ⊢ ⒶVs.ⓓ{a}ⓝW.V.T ➡*[h, g] U.
 #h #g #a #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_beta/
 #V0 #Vs #IHVs #V #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
 | #b #W1 #T1 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
-  [ elim (tstc_inv_bind_appls_simple … HT1) //
+  [ elim (tstc_inv_bind_applv_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV0.ⓛ{b}W1.T1)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
   ]
 | #b #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
-  [ elim (tstc_inv_bind_appls_simple … HT1) //
+  [ elim (tstc_inv_bind_applv_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV1.ⓓ{b}V3.T1)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
@@ -87,21 +87,21 @@ qed-.
 lemma cpxs_fwd_delta_vector: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
                              ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
                              ∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.#i ➡*[h, g] U →
-                             ⒶVs.#i ≃ U ∨ ⦃G, L⦄ ⊢ ⒶVs.V2 ➡*[h, g] U.
+                             ⒶVs.#i ≂ U ∨ ⦃G, L⦄ ⊢ ⒶVs.V2 ➡*[h, g] U.
 #h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs /2 width=5 by cpxs_fwd_delta/
 #V #Vs #IHVs #U #H -K -V1
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
 | #b #W0 #T0 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
-  [ elim (tstc_inv_bind_appls_simple … HT0) //
+  [ elim (tstc_inv_bind_applv_simple … HT0) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV.ⓛ{b}W0.T0)) /3 width=1 by cpxs_flat_dx, cpr_cpx, cpr_beta/
   ]
 | #b #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
-  [ elim (tstc_inv_bind_appls_simple … HT0) //
+  [ elim (tstc_inv_bind_applv_simple … HT0) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV0.ⓓ{b}V3.T0)) /3 width=3 by cpxs_flat, cpr_cpx, cpr_theta/
@@ -112,7 +112,7 @@ qed-.
 (* Basic_1: was just: pr3_iso_appls_abbr *)
 lemma cpxs_fwd_theta_vector: ∀h,g,G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
                              ∀a,V,T,U. ⦃G, L⦄ ⊢ ⒶV1s.ⓓ{a}V.T ➡*[h, g] U →
-                             ⒶV1s. ⓓ{a}V. T ≃ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}V.ⒶV2s.T ➡*[h, g] U.
+                             ⒶV1s. ⓓ{a}V. T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}V.ⒶV2s.T ➡*[h, g] U.
 #h #g #G #L #V1s #V2s * -V1s -V2s /3 width=1 by or_intror/
 #V1s #V2s #V1a #V2a #HV12a #HV12s #a
 generalize in match HV12a; -HV12a
@@ -145,11 +145,11 @@ elim (cpxs_inv_appl1 … H) -H *
     @(cpxs_trans … HU) -U
     elim (cpxs_inv_abbr1 … HT0) -HT0 *
     [ #V1 #T1 #HV1 #HT1 #H destruct
-      lapply (cpxs_lift … HV10a (L.ⓓV) (Ⓣ) … HV12a … HV0a) -V1a -V0a [ /2 width=1 by ldrop_drop/ ] #HV2a
+      lapply (cpxs_lift … HV10a (L.ⓓV) (Ⓕ) … HV12a … HV0a) -V1a -V0a [ /2 width=1 by drop_drop/ ] #HV2a
       @(cpxs_trans … (ⓓ{a}V.ⓐV2a.T1)) /3 width=1 by cpxs_bind, cpxs_pair_sn, cpxs_flat_dx, cpxs_bind_dx/
     | #X #HT1 #H #H0 destruct
       elim (lift_inv_bind1 … H) -H #V1 #T1 #HW01 #HT01 #H destruct
-      lapply (cpxs_lift … HV10a (L.ⓓV0) (Ⓣ) … HV12a … HV0a) -V0a [ /2 width=1 by ldrop_drop/ ] #HV2a
+      lapply (cpxs_lift … HV10a (L.ⓓV0) (Ⓕ) … HV12a … HV0a) -V0a [ /2 width=1 by drop_drop/ ] #HV2a
       @(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ{b}V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2s
       @(cpxs_strap2 … (ⓐV1a.ⓓ{b}V0.T0)) [ /4 width=7 by cpx_zeta, lift_bind, lift_flat/ ] -V -V1 -T1
       @(cpxs_strap2 … (ⓓ{b}V0.ⓐV2a.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpr_cpx, cpr_theta/
@@ -160,7 +160,7 @@ qed-.
 
 (* Basic_1: was just: pr3_iso_appls_cast *)
 lemma cpxs_fwd_cast_vector: ∀h,g,G,L,Vs,W,T,U. ⦃G, L⦄ ⊢ ⒶVs.ⓝW.T ➡*[h, g] U →
-                            ∨∨ ⒶVs. ⓝW. T ≃ U
+                            ∨∨ ⒶVs. ⓝW. T ≂ U
                              | ⦃G, L⦄ ⊢ ⒶVs.T ➡*[h, g] U
                              | ⦃G, L⦄ ⊢ ⒶVs.W ➡*[h, g] U.
 #h #g #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
@@ -168,7 +168,7 @@ lemma cpxs_fwd_cast_vector: ∀h,g,G,L,Vs,W,T,U. ⦃G, L⦄ ⊢ ⒶVs.ⓝW.T ➡
 elim (cpxs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or3_intro0/
 | #b #W0 #T0 #HT0 #HU elim (IHVs … HT0) -IHVs -HT0 #HT0
-  [ elim (tstc_inv_bind_appls_simple … HT0) //
+  [ elim (tstc_inv_bind_applv_simple … HT0) //
   | @or3_intro1 -W (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV.ⓛ{b}W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
@@ -178,7 +178,7 @@ elim (cpxs_inv_appl1 … H) -H *
   ]
 | #b #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
-  [ elim (tstc_inv_bind_appls_simple … HT0) //
+  [ elim (tstc_inv_bind_applv_simple … HT0) //
   | @or3_intro1 -W (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     @(cpxs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/