X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_tstc.ma;h=87ae419aac2e047c99b8fb8edeeb18a41f1af910;hb=f95f6cb21b86f3dad114b21f687aa5df36088064;hp=e8478aa84f36ad7d3796346cabd45d9bb339e576;hpb=ef49e0e7f5f298c299afdd3cbfdc2404ecb93879;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
index e8478aa84..87ae419aa 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
@@ -24,17 +24,32 @@ lemma cpxs_fwd_cnx: ∀h,g,L,T. ⦃h, L⦄ ⊢ 𝐍[g]⦃T⦄ → ∀U. ⦃h, L
 >(cpxs_inv_cnx1 … H HT) -L -T //
 qed-.
 
+lemma cpxs_fwd_sort: ∀h,g,L,U,k. ⦃h, L⦄ ⊢ ⋆k ➡*[g] U →
+                     ⋆k ≃ U ∨ ⦃h, L⦄ ⊢ ⋆(next h k) ➡*[g] U.
+#h #g #L #U #k #H
+elim (cpxs_inv_sort1 … H) -H #n #l generalize in match k; -k @(nat_ind_plus … n) -n
+[ #k #_ #H -l destruct /2 width=1/
+| #n #IHn #k >plus_plus_comm_23 #Hnl #H destruct
+  lapply (deg_next_SO … Hnl) -Hnl #Hnl
+  elim (IHn … Hnl) -IHn
+  [ #H lapply (tstc_inv_atom1 … H) -H #H >H -H /2 width=1/
+  | generalize in match Hnl; -Hnl @(nat_ind_plus … n) -n /2 width=1/
+    #n #_ /4 width=3/
+  | >iter_SO >iter_n_Sm //
+  ]
+]
+qed-.
+
 (* Basic_1: was just: pr3_iso_beta *)
 lemma cpxs_fwd_beta: ∀h,g,a,L,V,W,T,U. ⦃h, L⦄ ⊢ ⓐV.ⓛ{a}W.T ➡*[g] U →
-                     ⓐV.ⓛ{a}W.T ≃ U ∨ 
-                     ∃∃T0. ⦃h, L.ⓛW⦄ ⊢ T ➡*[g] T0 & ⦃h, L⦄ ⊢ ⓓ{a}V.T0 ➡*[g] U.
+                     ⓐV.ⓛ{a}W.T ≃ U ∨ ⦃h, L⦄ ⊢ ⓓ{a}ⓝW.V.T ➡*[g] U.
 #h #g #a #L #V #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #b #V0 #W0 #T0 #HV0 #HT0 #HU
-  elim (cpxs_inv_abst1 … HT0) -HT0 #W1 #T1 #_ #HT1 #H destruct -W1
-  @or_intror @(ex2_intro … HT1) -W (**) (* explicit constructors *)
-  @(cpxs_trans … HU) -U /2 width=1/
+| #b #W0 #T0 #HT0 #HU
+  elim (cpxs_inv_abst1 … HT0) -HT0 #W1 #T1 #HW1 #HT1 #H destruct
+  lapply (lsubr_cpxs_trans … HT1 (L.ⓓⓝW.V) ?) -HT1 /2 width=1/ #HT1
+  @or_intror @(cpxs_trans … HU) -U /3 width=1/ (**) (* explicit constructor *)  
 | #b #V1 #V2 #V0 #T1 #_ #_ #HT1 #_
   elim (cpxs_inv_abst1 … HT1) -HT1 #W2 #T2 #_ #_ #H destruct
 ]
@@ -58,15 +73,15 @@ lemma cpxs_fwd_theta: ∀h,g,a,L,V1,V,T,U. ⦃h, L⦄ ⊢ ⓐV1.ⓓ{a}V.T ➡*[g
 #h #g #a #L #V1 #V #T #U #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #b #V0 #W #T0 #HV10 #HT0 #HU
+| #b #W #T0 #HT0 #HU
   elim (cpxs_inv_abbr1 … HT0) -HT0 *
   [ #V3 #T3 #_ #_ #H destruct
   | #X #HT2 #H #H0 destruct
     elim (lift_inv_bind1 … H) -H #W2 #T2 #HW2 #HT02 #H destruct
     @or_intror @(cpxs_trans … HU) -U (**) (* explicit constructor *)
     @(cpxs_trans … (+ⓓV.ⓐV2.ⓛ{b}W2.T2)) [ /3 width=1/ ] -T
-    @(cpxs_strap2 … (ⓐV1.ⓛ{b}W.T0)) [ /5 width=7/ ] -V -V2 -W2 -T2
-    @(cpxs_strap2 … (ⓓ{b}V1.T0)) [ /3 width=1/ ] -W /2 width=1/
+    @(cpxs_strap2 … (ⓐV1.ⓛ{b}W.T0)) [2: /2 width=1/ ]
+    /4 width=7 by cpx_zeta, lift_bind, lift_flat/ (**) (* auto too slow without trace *) 
   ]
 | #b #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
   @or_intror @(cpxs_trans … HU) -U (**) (* explicit constructor *)
@@ -78,14 +93,14 @@ elim (cpxs_inv_appl1 … H) -H *
     elim (lift_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
     lapply (cpxs_lift … HV13 (L.ⓓV0) … HV12 … HV34) -V3 /2 width=1/ #HV24
     @(cpxs_trans … (+ⓓV.ⓐV2.ⓓ{b}V5.T5)) [ /3 width=1/ ] -T
-    @(cpxs_strap2 … (ⓐV1.ⓓ{b}V0.T0)) [ /5 width=7/ ] -V -V5 -T5
+    @(cpxs_strap2 … (ⓐV1.ⓓ{b}V0.T0)) [ /4 width=7 by cpx_zeta, lift_bind, lift_flat/ ] -V -V5 -T5 (**) (* auto too slow without trace *)
     @(cpxs_strap2 … (ⓓ{b}V0.ⓐV2.T0)) [ /3 width=3/ ] -V1 /3 width=1/
   ]
 ]
 qed-.
 
-lemma cpxs_fwd_tau: ∀h,g,L,W,T,U. ⦃h, L⦄ ⊢ ⓝW.T ➡*[g] U →
-                    ⓝW. T ≃ U ∨ ⦃h, L⦄ ⊢ T ➡*[g] U.
+lemma cpxs_fwd_cast: ∀h,g,L,W,T,U. ⦃h, L⦄ ⊢ ⓝW.T ➡*[g] U →
+                     ∨∨ ⓝW. T ≃ U | ⦃h, L⦄ ⊢ T ➡*[g] U | ⦃h, L⦄ ⊢ W ➡*[g] U.
 #h #g #L #W #T #U #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1/