- we introduced the pointer_step rc in the perspective of proving

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / cprs_tstc_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
index a6aedd7994aed73181c551882ca7a2edc3d074a0..fd3eb585e2e97d1ae456f82f56aa1dd8654cf174 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
@@ -26,35 +26,35 @@ lemma cprs_fwd_cnf_vector: ∀L,T.  𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ → ∀Vs,
 #V #Vs #IHVs #U #H
 elim (cprs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0 #W0 #T0 #HV0 #HT0 #HU
+| #a #V0 #W0 #T0 #HV0 #HT0 #HU
   lapply (IHVs … HT0) -IHVs -HT0 #HT0
   elim (tstc_inv_bind_appls_simple … HT0 ?) //
-| #V1 #V2 #V0 #T0 #HV1 #HV12 #HT0 #HU
+| #a #V1 #V2 #V0 #T0 #HV1 #HV12 #HT0 #HU
   lapply (IHVs … HT0) -IHVs -HT0 #HT0
   elim (tstc_inv_bind_appls_simple … HT0 ?) //
 ]
 qed-.
 
 (* Basic_1: was: pr3_iso_appls_beta *)
-lemma cprs_fwd_beta_vector: ∀L,Vs,V,W,T,U. L ⊢ ⒶVs. ⓐV. ⓛW. T ➡* U →
-                            ⒶVs. ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⒶVs. ⓓV. T ➡* U.
-#L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_beta/
+lemma cprs_fwd_beta_vector: ∀a,L,Vs,V,W,T,U. L ⊢ ⒶVs. ⓐV. ⓛ{a}W. T ➡* U →
+                            ⒶVs. ⓐV. ⓛ{a}W. T ≃ U ∨ L ⊢ ⒶVs. ⓓ{a}V. T ➡* U.
+#a #L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_beta/
 #V0 #Vs #IHVs #V #W #T #U #H
 elim (cprs_inv_appl1 … H) -H *
 [ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1/
-| #V1 #W1 #T1 #HV01 #HT1 #HU
+| #b #V1 #W1 #T1 #HV01 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
   [ elim (tstc_inv_bind_appls_simple … HT1 ?) //
   | @or_intror -W (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV1.ⓛW1.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=1/
+    @(cprs_strap1 … (ⓐV1.ⓛ{b}W1.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=1/
   ]
-| #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
+| #b #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
   [ elim (tstc_inv_bind_appls_simple … HT1 ?) //
   | @or_intror -W (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV1.ⓓV3.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=3/
+    @(cprs_strap1 … (ⓐV1.ⓓ{b}V3.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=3/
   ]
 ]
 qed-.
@@ -67,29 +67,29 @@ lemma cprs_fwd_delta_vector: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
 #V #Vs #IHVs #U #H -K -V1
 elim (cprs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0 #W0 #T0 #HV0 #HT0 #HU
+| #b #V0 #W0 #T0 #HV0 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=1/
+    @(cprs_strap1 … (ⓐV0.ⓛ{b}W0.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=1/
   ]
-| #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
+| #b #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV0.ⓓV3.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=3/
+    @(cprs_strap1 … (ⓐV0.ⓓ{b}V3.T0)) [ /2 width=1/ ] -V -V2 -Vs /3 width=3/
   ]
 ]
 qed-.
 
 (* Basic_1: was: pr3_iso_appls_abbr *)
 lemma cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                             ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
-                             ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
+                             ∀a,V,T,U. L ⊢ ⒶV1s. ⓓ{a}V. T ➡* U →
+                             ⒶV1s. ⓓ{a}V. T ≃ U ∨ L ⊢ ⓓ{a}V. ⒶV2s. T ➡* U.
 #L #V1s #V2s * -V1s -V2s /3 width=1/
-#V1s #V2s #V1a #V2a #HV12a #HV12s
+#V1s #V2s #V1a #V2a #HV12a #HV12s #a
 generalize in match HV12a; -HV12a
 generalize in match V2a; -V2a
 generalize in match V1a; -V1a
@@ -97,7 +97,7 @@ elim HV12s -V1s -V2s /2 width=1 by cprs_fwd_theta/
 #V1s #V2s #V1b #V2b #HV12b #_ #IHV12s #V1a #V2a #HV12a #V #T #U #H
 elim (cprs_inv_appl1 … H) -H *
 [ -IHV12s -HV12a -HV12b #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0a #W0 #T0 #HV10a #HT0 #HU
+| #b #V0a #W0 #T0 #HV10a #HT0 #HU
   elim (IHV12s … HV12b … HT0) -IHV12s -HT0 #HT0
   [ -HV12a -HV12b -HV10a -HU
     elim (tstc_inv_pair1 … HT0) #V1 #T1 #H destruct
@@ -105,14 +105,14 @@ elim (cprs_inv_appl1 … H) -H *
     @(cprs_trans … HU) -U
     elim (cprs_inv_abbr1 … HT0) -HT0 *
     [ -HV12a -HV12b -HV10a #V1 #T1 #_ #_ #H destruct
-    | -V1b #X #HT1 #H
+    | -V1b #X #HT1 #H #H0 destruct
       elim (lift_inv_bind1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
-      @(cprs_trans … (ⓓV.ⓐV2a.ⓛW1.T1)) [ /3 width=1/ ] -T -V2b -V2s
-      @(cprs_strap2 … (ⓐV1a.ⓛW0.T0)) [ /5 width=7/ ] -V -V2a -W1 -T1
-      @(cprs_strap2 … (ⓓV1a.T0)) [ /3 width=1/ ] -W0 /2 width=1/
+      @(cprs_trans … (+ⓓV.ⓐV2a.ⓛ{b}W1.T1)) [ /3 width=1/ ] -T -V2b -V2s
+      @(cprs_strap2 … (ⓐV1a.ⓛ{b}W0.T0)) [ /5 width=7/ ] -V -V2a -W1 -T1
+      @(cprs_strap2 … (ⓓ{b}V1a.T0)) [ /3 width=1/ ] -W0 /2 width=1/
     ]
   ]
-| #V0a #Va #V0 #T0 #HV10a #HV0a #HT0 #HU
+| #b #V0a #Va #V0 #T0 #HV10a #HV0a #HT0 #HU
   elim (IHV12s … HV12b … HT0) -HV12b -IHV12s -HT0 #HT0
   [ -HV12a -HV10a -HV0a -HU
     elim (tstc_inv_pair1 … HT0) #V1 #T1 #H destruct
@@ -121,13 +121,13 @@ elim (cprs_inv_appl1 … H) -H *
     elim (cprs_inv_abbr1 … HT0) -HT0 *
     [ #V1 #T1 #HV1 #HT1 #H destruct
       lapply (cprs_lift (L.ⓓV) … HV12a … HV10a … HV0a) -V1a -V0a [ /2 width=1/ ] #HV2a
-      @(cprs_trans … (ⓓV.ⓐV2a.T1)) [ /3 width=1/ ] -T -V2b -V2s /3 width=1/
-    | #X #HT1 #H
+      @(cprs_trans … (ⓓ{a}V.ⓐV2a.T1)) [ /3 width=1/ ] -T -V2b -V2s /3 width=1/
+    | #X #HT1 #H #H0 destruct
       elim (lift_inv_bind1 … H) -H #V1 #T1 #HW01 #HT01 #H destruct
       lapply (cprs_lift (L.ⓓV0) … HV12a … HV10a … HV0a) -V0a [ /2 width=1/ ] #HV2a
-      @(cprs_trans … (ⓓV.ⓐV2a.ⓓV1.T1)) [ /3 width=1/ ] -T -V2b -V2s
-      @(cprs_strap2 … (ⓐV1a.ⓓV0.T0)) [ /5 width=7/ ] -V -V1 -T1
-      @(cprs_strap2 … (ⓓV0.ⓐV2a.T0)) [ /3 width=3/ ] -V1a /3 width=1/
+      @(cprs_trans … (+ⓓV.ⓐV2a.ⓓ{b}V1.T1)) [ /3 width=1/ ] -T -V2b -V2s
+      @(cprs_strap2 … (ⓐV1a.ⓓ{b}V0.T0)) [ /5 width=7/ ] -V -V1 -T1
+      @(cprs_strap2 … (ⓓ{b}V0.ⓐV2a.T0)) [ /3 width=3/ ] -V1a /3 width=1/
     ]
   ]
 ]  
@@ -140,18 +140,18 @@ lemma cprs_fwd_tau_vector: ∀L,Vs,W,T,U. L ⊢ ⒶVs. ⓝW. T ➡* U →
 #V #Vs #IHVs #W #T #U #H
 elim (cprs_inv_appl1 … H) -H *
 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0 #W0 #T0 #HV0 #HT0 #HU
+| #b #V0 #W0 #T0 #HV0 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
   | @or_intror -W (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=1/
+    @(cprs_strap1 … (ⓐV0.ⓛ{b}W0.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=1/
   ]
-| #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
+| #b #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
   | @or_intror -W (**) (* explicit constructor *)
     @(cprs_trans … HU) -U
-    @(cprs_strap1 … (ⓐV0.ⓓV2.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=3/
+    @(cprs_strap1 … (ⓐV0.ⓓ{b}V2.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=3/
 ]
 qed-.