- degree-based equivalene for terms

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts_vector.ma
index e82935af4c0a11013f38e9bc3494aef087809850..6252ed90eae75ba248f860f05d52a673e2745c49 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts_vector.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/tsts_vector.ma".
+include "basic_2/syntax/tsts_vector.ma".
 include "basic_2/substitution/lift_vector.ma".
 include "basic_2/computation/cpxs_tsts.ma".
 
@@ -21,8 +21,8 @@ include "basic_2/computation/cpxs_tsts.ma".
 (* Vector form of forward lemmas involving same top term structure **********)
 
 (* Basic_1: was just: nf2_iso_appls_lref *)
-lemma cpxs_fwd_cnx_vector: â\88\80h,o,G,L,T.  ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, o] 𝐍⦃T⦄ →
-                           â\88\80Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.T â\9e¡*[h, o] U → ⒶVs.T ≂ U.
+lemma cpxs_fwd_cnx_vector: â\88\80h,o,G,L,T.  ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\88[h, o] 𝐍⦃T⦄ →
+                           â\88\80Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.T â¬\88*[h, o] U → ⒶVs.T ≂ U.
 #h #o #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 *
@@ -36,8 +36,8 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_sort_vector: â\88\80h,o,G,L,s,Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\8b\86s â\9e¡*[h, o] U →
-                            â\92¶Vs.â\8b\86s â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\8b\86(next h s) â\9e¡*[h, o] U.
+lemma cpxs_fwd_sort_vector: â\88\80h,o,G,L,s,Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\8b\86s â¬\88*[h, o] U →
+                            â\92¶Vs.â\8b\86s â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\8b\86(next h s) â¬\88*[h, o] U.
 #h #o #G #L #s #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_sort/
 #V #Vs #IHVs #U #H
 elim (cpxs_inv_appl1 … H) -H *
@@ -61,8 +61,8 @@ qed-.
 
 
 (* Basic_1: was just: pr3_iso_appls_beta *)
-lemma cpxs_fwd_beta_vector: â\88\80h,o,a,G,L,Vs,V,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\90V.â\93\9b{a}W.T â\9e¡*[h, o] U →
-                            â\92¶Vs. â\93\90V. â\93\9b{a}W. T â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\93{a}â\93\9dW.V.T â\9e¡*[h, o] U.
+lemma cpxs_fwd_beta_vector: â\88\80h,o,a,G,L,Vs,V,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\90V.â\93\9b{a}W.T â¬\88*[h, o] U →
+                            â\92¶Vs. â\93\90V. â\93\9b{a}W. T â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\93{a}â\93\9dW.V.T â¬\88*[h, o] U.
 #h #o #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 *
@@ -86,8 +86,8 @@ qed-.
 
 lemma cpxs_fwd_delta_vector: ∀h,o,I,G,L,K,V1,i. ⬇[i] L ≡ K.ⓑ{I}V1 →
                              ∀V2. ⬆[0, i + 1] V1 ≡ V2 →
-                             â\88\80Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.#i â\9e¡*[h, o] U →
-                             â\92¶Vs.#i â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.V2 â\9e¡*[h, o] U.
+                             â\88\80Vs,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.#i â¬\88*[h, o] U →
+                             â\92¶Vs.#i â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.V2 â¬\88*[h, o] U.
 #h #o #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 *
@@ -110,38 +110,38 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 (* Basic_1: was just: pr3_iso_appls_abbr *)
-lemma cpxs_fwd_theta_vector: ∀h,o,G,L,V1c,V2c. ⬆[0, 1] V1c ≡ V2c →
-                             ∀a,V,T,U. ⦃G, L⦄ ⊢ ⒶV1c.ⓓ{a}V.T ➡*[h, o] U →
-                             ⒶV1c. ⓓ{a}V. T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}V.ⒶV2c.T ➡*[h, o] U.
-#h #o #G #L #V1c #V2c * -V1c -V2c /3 width=1 by or_intror/
-#V1c #V2c #V1a #V2a #HV12a #HV12c #a
+lemma cpxs_fwd_theta_vector: ∀h,o,G,L,V1b,V2b. ⬆[0, 1] V1b ≡ V2b →
+                             ∀a,V,T,U. ⦃G, L⦄ ⊢ ⒶV1b.ⓓ{a}V.T ⬈*[h, o] U →
+                             ⒶV1b. ⓓ{a}V. T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}V.ⒶV2b.T ⬈*[h, o] U.
+#h #o #G #L #V1b #V2b * -V1b -V2b /3 width=1 by or_intror/
+#V1b #V2b #V1a #V2a #HV12a #HV12b #a
 generalize in match HV12a; -HV12a
 generalize in match V2a; -V2a
 generalize in match V1a; -V1a
-elim HV12c -V1c -V2c /2 width=1 by cpxs_fwd_theta/
-#V1c #V2c #V1b #V2b #HV12b #_ #IHV12c #V1a #V2a #HV12a #V #T #U #H
+elim HV12b -V1b -V2b /2 width=1 by cpxs_fwd_theta/
+#V1b #V2b #V1b #V2b #HV12b #_ #IHV12b #V1a #V2a #HV12a #V #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
-[ -IHV12c -HV12a -HV12b #V0 #T0 #_ #_ #H destruct /2 width=1 by tsts_pair, or_introl/
+[ -IHV12b -HV12a -HV12b #V0 #T0 #_ #_ #H destruct /2 width=1 by tsts_pair, or_introl/
 | #b #W0 #T0 #HT0 #HU
-  elim (IHV12c … HV12b … HT0) -IHV12c -HT0 #HT0
+  elim (IHV12b … HV12b … HT0) -IHV12b -HT0 #HT0
   [ -HV12a -HV12b -HU
     elim (tsts_inv_pair1 … HT0) #V1 #T1 #H destruct
-  | @or_intror -V1c (**) (* explicit constructor *)
+  | @or_intror -V1b (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     elim (cpxs_inv_abbr1 … HT0) -HT0 *
     [ -HV12a -HV12b #V1 #T1 #_ #_ #H destruct
     | -V1b #X #HT1 #H #H0 destruct
       elim (lift_inv_bind1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
-      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓛ{b}W1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2c
+      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓛ{b}W1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
       @(cpxs_strap2 … (ⓐV1a.ⓛ{b}W0.T0))
       /4 width=7 by cpxs_beta_dx, cpx_zeta, lift_bind, lift_flat/
     ]
   ]
 | #b #V0a #Va #V0 #T0 #HV10a #HV0a #HT0 #HU
-  elim (IHV12c … HV12b … HT0) -HV12b -IHV12c -HT0 #HT0
+  elim (IHV12b … HV12b … HT0) -HV12b -IHV12b -HT0 #HT0
   [ -HV12a -HV10a -HV0a -HU
     elim (tsts_inv_pair1 … HT0) #V1 #T1 #H destruct
-  | @or_intror -V1c -V1b (**) (* explicit constructor *)
+  | @or_intror -V1b -V1b (**) (* explicit constructor *)
     @(cpxs_trans … HU) -U
     elim (cpxs_inv_abbr1 … HT0) -HT0 *
     [ #V1 #T1 #HV1 #HT1 #H destruct
@@ -150,7 +150,7 @@ elim (cpxs_inv_appl1 … H) -H *
     | #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 drop_drop/ ] #HV2a
-      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ{b}V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2c
+      @(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ{b}V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
       @(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/
     ]
@@ -159,10 +159,10 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 (* Basic_1: was just: pr3_iso_appls_cast *)
-lemma cpxs_fwd_cast_vector: â\88\80h,o,G,L,Vs,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\9dW.T â\9e¡*[h, o] U →
+lemma cpxs_fwd_cast_vector: â\88\80h,o,G,L,Vs,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.â\93\9dW.T â¬\88*[h, o] U →
                             ∨∨ ⒶVs. ⓝW. T ≂ U
-                             | â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.T â\9e¡*[h, o] U
-                             | â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.W â\9e¡*[h, o] U.
+                             | â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.T â¬\88*[h, o] U
+                             | â¦\83G, Lâ¦\84 â\8a¢ â\92¶Vs.W â¬\88*[h, o] U.
 #h #o #G #L #Vs elim Vs -Vs /2 width=1 by cpxs_fwd_cast/
 #V #Vs #IHVs #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *