update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_teqo_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
index 5b7135b0113f6e71bf79fa4ff3ff29a0d7fa4faa..4962015793e08ee8757a34cdf78d35ab37338ade 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqo_vector.ma
@@ -21,7 +21,7 @@ include "basic_2/rt_computation/cpxs_teqo.ma".
 (* Vector form of forward lemmas with outer equivalence for terms ***********)
 
 lemma cpxs_fwd_sort_vector (h) (G) (L):
-      â\88\80s,Vs,X2. â¦\83G,Lâ¦\84 ⊢ ⒶVs.⋆s ⬈*[h] X2 → ⒶVs.⋆s ⩳ X2.
+      â\88\80s,Vs,X2. â\9dªG,Lâ\9d« ⊢ ⒶVs.⋆s ⬈*[h] X2 → ⒶVs.⋆s ⩳ X2.
 #h #G #L #s #Vs elim Vs -Vs /2 width=4 by cpxs_fwd_sort/
 #V #Vs #IHVs #X2 #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -37,10 +37,10 @@ qed-.
 
 (* Basic_2A1: was: cpxs_fwd_delta_vector *)
 lemma cpxs_fwd_delta_drops_vector (h) (I) (G) (L) (K):
-      ∀V1,i. ⇩*[i] L ≘ K.ⓑ{I}V1 →
+      ∀V1,i. ⇩*[i] L ≘ K.ⓑ[I]V1 →
       ∀V2. ⇧*[↑i] V1 ≘ V2 →
-      â\88\80Vs,X2. â¦\83G,Lâ¦\84 ⊢ ⒶVs.#i ⬈*[h] X2 →
-      â\88¨â\88¨ â\92¶Vs.#i ⩳ X2 | â¦\83G,Lâ¦\84 ⊢ ⒶVs.V2 ⬈*[h] X2.
+      â\88\80Vs,X2. â\9dªG,Lâ\9d« ⊢ ⒶVs.#i ⬈*[h] X2 →
+      â\88¨â\88¨ â\92¶Vs.#i ⩳ X2 | â\9dªG,Lâ\9d« ⊢ ⒶVs.V2 ⬈*[h] X2.
 #h #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs
 elim Vs -Vs /2 width=5 by cpxs_fwd_delta_drops/
 #V #Vs #IHVs #X2 #H -K -V1
@@ -51,22 +51,22 @@ elim (cpxs_inv_appl1 … H) -H *
   [ elim (teqo_inv_applv_bind_simple … HT0) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV.ⓛ{q}W0.T0)) /3 width=1 by cpxs_flat_dx, cpx_beta/
+    @(cpxs_strap1 … (ⓐV.ⓛ[q]W0.T0)) /3 width=1 by cpxs_flat_dx, cpx_beta/
   ]
 | #q #V0 #V1 #V3 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (teqo_inv_applv_bind_simple … HT0) //
   | @or_intror -i (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV0.ⓓ{q}V3.T0)) /3 width=3 by cpxs_flat, cpx_theta/
+    @(cpxs_strap1 … (ⓐV0.ⓓ[q]V3.T0)) /3 width=3 by cpxs_flat, cpx_theta/
   ]
 ]
 qed-.
 
 (* Basic_1: was just: pr3_iso_appls_beta *)
 lemma cpxs_fwd_beta_vector (h) (p) (G) (L):
-      â\88\80Vs,V,W,T,X2. â¦\83G,Lâ¦\84 â\8a¢ â\92¶Vs.â\93\90V.â\93\9b{p}W.T ⬈*[h] X2 →
-      ∨∨ ⒶVs.ⓐV.ⓛ{p}W. T ⩳ X2 | ⦃G,L⦄ ⊢ ⒶVs.ⓓ{p}ⓝW.V.T ⬈*[h] X2.
+      â\88\80Vs,V,W,T,X2. â\9dªG,Lâ\9d« â\8a¢ â\92¶Vs.â\93\90V.â\93\9b[p]W.T ⬈*[h] X2 →
+      ∨∨ ⒶVs.ⓐV.ⓛ[p]W. T ⩳ X2 | ❪G,L❫ ⊢ ⒶVs.ⓓ[p]ⓝW.V.T ⬈*[h] X2.
 #h #p #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_beta/
 #V0 #Vs #IHVs #V #W #T #X2 #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -76,14 +76,14 @@ elim (cpxs_inv_appl1 … H) -H *
   [ elim (teqo_inv_applv_bind_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV0.ⓛ{q}W1.T1)) /3 width=1 by cpxs_flat_dx, cpx_beta/
+    @(cpxs_strap1 … (ⓐV0.ⓛ[q]W1.T1)) /3 width=1 by cpxs_flat_dx, cpx_beta/
   ]
 | #q #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
   elim (IHVs … HT1) -IHVs -HT1 #HT1
   [ elim (teqo_inv_applv_bind_simple … HT1) //
   | @or_intror (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV1.ⓓ{q}V3.T1)) /3 width=3 by cpxs_flat, cpx_theta/
+    @(cpxs_strap1 … (ⓐV1.ⓓ[q]V3.T1)) /3 width=3 by cpxs_flat, cpx_theta/
   ]
 ]
 qed-.
@@ -91,8 +91,8 @@ qed-.
 (* Basic_1: was just: pr3_iso_appls_abbr *)
 lemma cpxs_fwd_theta_vector (h) (G) (L):
       ∀V1b,V2b. ⇧*[1] V1b ≘ V2b →
-      â\88\80p,V,T,X2. â¦\83G,Lâ¦\84 â\8a¢ â\92¶V1b.â\93\93{p}V.T ⬈*[h] X2 →
-      ∨∨ ⒶV1b.ⓓ{p}V.T ⩳ X2 | ⦃G,L⦄ ⊢ ⓓ{p}V.ⒶV2b.T ⬈*[h] X2.
+      â\88\80p,V,T,X2. â\9dªG,Lâ\9d« â\8a¢ â\92¶V1b.â\93\93[p]V.T ⬈*[h] X2 →
+      ∨∨ ⒶV1b.ⓓ[p]V.T ⩳ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⒶV2b.T ⬈*[h] X2.
 #h #G #L #V1b #V2b * -V1b -V2b /3 width=1 by or_intror/
 #V1b #V2b #V1a #V2a #HV12a #HV12b #p
 generalize in match HV12a; -HV12a
@@ -112,8 +112,8 @@ elim (cpxs_inv_appl1 … H) -H *
     [ -HV12a #V1 #T1 #_ #_ #H destruct
     | -V1b #X #HT1 #H #H0 destruct
       elim (lifts_inv_bind1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
-      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓛ{q}W1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
-      @(cpxs_strap2 … (ⓐV1a.ⓛ{q}W0.T0))
+      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓛ[q]W1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
+      @(cpxs_strap2 … (ⓐV1a.ⓛ[q]W0.T0))
       /4 width=7 by cpxs_beta_dx, cpx_zeta, lifts_bind, lifts_flat/
     ]
   ]
@@ -126,13 +126,13 @@ elim (cpxs_inv_appl1 … H) -H *
     elim (cpxs_inv_abbr1_dx … HT0) -HT0 *
     [ #V1 #T1 #HV1 #HT1 #H destruct
       lapply (cpxs_lifts_bi … HV10a (Ⓣ) … (L.ⓓV) … HV12a … HV0a) -V1a -V0a /3 width=1 by drops_refl, drops_drop/ #HV2a
-      @(cpxs_trans … (ⓓ{p}V.ⓐV2a.T1)) /3 width=1 by cpxs_bind, cpxs_pair_sn, cpxs_flat_dx, cpxs_bind_dx/
+      @(cpxs_trans … (ⓓ[p]V.ⓐV2a.T1)) /3 width=1 by cpxs_bind, cpxs_pair_sn, cpxs_flat_dx, cpxs_bind_dx/
     | #X #HT1 #H #H0 destruct
       elim (lifts_inv_bind1 … H) -H #V1 #T1 #HW01 #HT01 #H destruct
       lapply (cpxs_lifts_bi … HV10a (Ⓣ) … (L.ⓓV0) … HV12a … HV0a) -V0a /3 width=1 by drops_refl, drops_drop/ #HV2a
-      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ{q}V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
-      @(cpxs_strap2 … (ⓐV1a.ⓓ{q}V0.T0)) [ /4 width=7 by cpx_zeta, lifts_bind, lifts_flat/ ] -V -V1 -T1
-      @(cpxs_strap2 … (ⓓ{q}V0.ⓐV2a.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpx_theta/
+      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ[q]V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
+      @(cpxs_strap2 … (ⓐV1a.ⓓ[q]V0.T0)) [ /4 width=7 by cpx_zeta, lifts_bind, lifts_flat/ ] -V -V1 -T1
+      @(cpxs_strap2 … (ⓓ[q]V0.ⓐV2a.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpx_theta/
     ]
   ]
 ]
@@ -140,10 +140,10 @@ qed-.
 
 (* Basic_1: was just: pr3_iso_appls_cast *)
 lemma cpxs_fwd_cast_vector (h) (G) (L):
-      â\88\80Vs,W,T,X2. â¦\83G,Lâ¦\84 ⊢ ⒶVs.ⓝW.T ⬈*[h] X2 →
+      â\88\80Vs,W,T,X2. â\9dªG,Lâ\9d« ⊢ ⒶVs.ⓝW.T ⬈*[h] X2 →
       ∨∨ ⒶVs. ⓝW. T ⩳ X2
-       | â¦\83G,Lâ¦\84 ⊢ ⒶVs.T ⬈*[h] X2
-       | â¦\83G,Lâ¦\84 ⊢ ⒶVs.W ⬈*[h] X2.
+       | â\9dªG,Lâ\9d« ⊢ ⒶVs.T ⬈*[h] X2
+       | â\9dªG,Lâ\9d« ⊢ ⒶVs.W ⬈*[h] X2.
 #h #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
 #V #Vs #IHVs #W #T #X2 #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -152,28 +152,28 @@ elim (cpxs_inv_appl1 … H) -H *
   [ elim (teqo_inv_applv_bind_simple … HT0) //
   | @or3_intro1 -W (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV.ⓛ{q}W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
+    @(cpxs_strap1 … (ⓐV.ⓛ[q]W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
   | @or3_intro2 -T (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV.ⓛ{q}W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
+    @(cpxs_strap1 … (ⓐV.ⓛ[q]W0.T0)) /2 width=1 by cpxs_flat_dx, cpx_beta/
   ]
 | #q #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (teqo_inv_applv_bind_simple … HT0) //
   | @or3_intro1 -W (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV0.ⓓ{q}V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/
+    @(cpxs_strap1 … (ⓐV0.ⓓ[q]V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/
   | @or3_intro2 -T (**) (* explicit constructor *)
     @(cpxs_trans … HU) -X2
-    @(cpxs_strap1 … (ⓐV0.ⓓ{q}V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/
+    @(cpxs_strap1 … (ⓐV0.ⓓ[q]V2.T0)) /2 width=3 by cpxs_flat, cpx_theta/
   ]
 ]
 qed-.
 
 (* Basic_1: was just: nf2_iso_appls_lref *)
 lemma cpxs_fwd_cnx_vector (h) (G) (L):
-      â\88\80T. ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88[h] ð\9d\90\8dâ¦\83Tâ¦\84 →
-      â\88\80Vs,X2. â¦\83G,Lâ¦\84 ⊢ ⒶVs.T ⬈*[h] X2 → ⒶVs.T ⩳ X2.
+      â\88\80T. ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d« →
+      â\88\80Vs,X2. â\9dªG,Lâ\9d« ⊢ ⒶVs.T ⬈*[h] X2 → ⒶVs.T ⩳ X2.
 #h #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 #X2 #H
 elim (cpxs_inv_appl1 … H) -H *