X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Funfold%2Flstas_da.ma;h=6ecadc335b0f503856c5264787ac89d5afb92170;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=8d1feca9f9e09032abb2970e56812406b55e3281;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_da.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_da.ma
index 8d1feca9f..6ecadc335 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_da.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lstas_da.ma
@@ -19,77 +19,77 @@ include "basic_2/unfold/lstas_lstas.ma".
 
 (* Properties on degree assignment for terms ********************************)
 
-lemma da_lstas: ∀h,g,G,L,T,l1. ⦃G, L⦄ ⊢ T ▪[h, g] l1 → ∀l2.
-                ∃∃U. ⦃G, L⦄ ⊢ T •*[h, l2] U & ⦃G, L⦄ ⊢ U ▪[h, g] l1-l2.
-#h #g #G #L #T #l1 #H elim H -G -L -T -l1
+lemma da_lstas: ∀h,g,G,L,T,d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 → ∀d2.
+                ∃∃U. ⦃G, L⦄ ⊢ T •*[h, d2] U & ⦃G, L⦄ ⊢ U ▪[h, g] d1-d2.
+#h #g #G #L #T #d1 #H elim H -G -L -T -d1
 [ /4 width=3 by da_sort, deg_iter, ex2_intro/
-| #G #L #K #V #i #l1 #HLK #_ #IHV #l2
-  elim (IHV l2) -IHV #W
+| #G #L #K #V #i #d1 #HLK #_ #IHV #d2
+  elim (IHV d2) -IHV #W
   elim (lift_total W 0 (i+1))
   lapply (drop_fwd_drop2 … HLK)
   /3 width=10 by lstas_ldef, da_lift, ex2_intro/
-| #G #L #K #W #i #l1 #HLK #HW #IHW #l2 @(nat_ind_plus … l2) -l2
+| #G #L #K #W #i #d1 #HLK #HW #IHW #d2 @(nat_ind_plus … d2) -d2
   [ elim (IHW 0) -IHW /3 width=6 by lstas_zero, da_ldec, ex2_intro/
-  | #l #_ elim (IHW l) -IHW #V
+  | #d #_ elim (IHW d) -IHW #V
     elim (lift_total V 0 (i+1))
     lapply (drop_fwd_drop2 … HLK)
     /3 width=10 by lstas_succ, da_lift, ex2_intro/
   ]
-| #a #I #G #L #V #T #l1 #_ #IHT #l2 elim (IHT … l2) -IHT
+| #a #I #G #L #V #T #d1 #_ #IHT #d2 elim (IHT … d2) -IHT
   /3 width=6 by lstas_bind, da_bind, ex2_intro/
-| * #G #L #V #T #l1 #_ #IHT #l2 elim (IHT … l2) -IHT
+| * #G #L #V #T #d1 #_ #IHT #d2 elim (IHT … d2) -IHT
   /3 width=5 by lstas_appl, lstas_cast, da_flat, ex2_intro/
 ]
 qed-.
 
-lemma lstas_da_conf: ∀h,g,G,L,T,U,l2. ⦃G, L⦄ ⊢ T •*[h, l2] U →
-                     ∀l1. ⦃G, L⦄ ⊢ T ▪[h, g] l1 → ⦃G, L⦄ ⊢ U ▪[h, g] l1-l2.
-#h #g #G #L #T #U #l2 #HTU #l1 #HT
-elim (da_lstas … HT l2) -HT #X #HTX
+lemma lstas_da_conf: ∀h,g,G,L,T,U,d2. ⦃G, L⦄ ⊢ T •*[h, d2] U →
+                     ∀d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 → ⦃G, L⦄ ⊢ U ▪[h, g] d1-d2.
+#h #g #G #L #T #U #d2 #HTU #d1 #HT
+elim (da_lstas … HT d2) -HT #X #HTX
 lapply (lstas_mono … HTX … HTU) -T //
 qed-.
 
 (* inversion lemmas on degree assignment for terms **************************)
 
-lemma lstas_inv_da: ∀h,g,G,L,T,U,l2. ⦃G, L⦄ ⊢ T •*[h, l2] U →
-                    ∃∃l1. ⦃G, L⦄ ⊢ T ▪[h, g] l1 & ⦃G, L⦄ ⊢ U ▪[h, g] l1-l2.
-#h #g #G #L #T #U #l2 #H elim H -G -L -T -U -l2
-[ #G #L #l2 #k elim (deg_total h g k) /4 width=3 by da_sort, deg_iter, ex2_intro/
-| #G #L #K #V #W #U #i #l2 #HLK #_ #HWU *
+lemma lstas_inv_da: ∀h,g,G,L,T,U,d2. ⦃G, L⦄ ⊢ T •*[h, d2] U →
+                    ∃∃d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 & ⦃G, L⦄ ⊢ U ▪[h, g] d1-d2.
+#h #g #G #L #T #U #d2 #H elim H -G -L -T -U -d2
+[ #G #L #d2 #k elim (deg_total h g k) /4 width=3 by da_sort, deg_iter, ex2_intro/
+| #G #L #K #V #W #U #i #d2 #HLK #_ #HWU *
   lapply (drop_fwd_drop2 … HLK) /3 width=10 by da_lift, da_ldef, ex2_intro/
 | #G #L #K #W #V #i #HLK #_ * /3 width=6 by da_ldec, ex2_intro/
-| #G #L #K #W #V #U #i #l2 #HLK #_ #HVU *
+| #G #L #K #W #V #U #i #d2 #HLK #_ #HVU *
   lapply (drop_fwd_drop2 … HLK) /3 width=10 by da_lift, da_ldec, ex2_intro/
-| #a #I #G #L #V #T #U #l2 #_ * /3 width=3 by da_bind, ex2_intro/
-| #G #L #V #T #U #l2 #_ * /3 width=3 by da_flat, ex2_intro/
-| #G #L #W #T #U #l2 #_ * /3 width=3 by da_flat, ex2_intro/
+| #a #I #G #L #V #T #U #d2 #_ * /3 width=3 by da_bind, ex2_intro/
+| #G #L #V #T #U #d2 #_ * /3 width=3 by da_flat, ex2_intro/
+| #G #L #W #T #U #d2 #_ * /3 width=3 by da_flat, ex2_intro/
 ]
 qed-.
 
-lemma lstas_inv_da_ge: ∀h,G,L,T,U,l2,l. ⦃G, L⦄ ⊢ T •*[h, l2] U →
-                       ∃∃g,l1. ⦃G, L⦄ ⊢ T ▪[h, g] l1 & ⦃G, L⦄ ⊢ U ▪[h, g] l1-l2 & l ≤ l1.
-#h #G #L #T #U #l2 #l #H elim H -G -L -T -U -l2
+lemma lstas_inv_da_ge: ∀h,G,L,T,U,d2,d. ⦃G, L⦄ ⊢ T •*[h, d2] U →
+                       ∃∃g,d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 & ⦃G, L⦄ ⊢ U ▪[h, g] d1-d2 & d ≤ d1.
+#h #G #L #T #U #d2 #d #H elim H -G -L -T -U -d2
 [ /4 width=5 by da_sort, deg_iter, ex3_2_intro/
-| #G #L #K #V #W #U #i #l2 #HLK #_ #HWU *
+| #G #L #K #V #W #U #i #d2 #HLK #_ #HWU *
   lapply (drop_fwd_drop2 … HLK) /3 width=10 by da_lift, da_ldef, ex3_2_intro/
 | #G #L #K #W #V #i #HLK #_ * 
-  #g #l1 #HW #HV #Hl1 /4 width=6 by da_ldec, lt_to_le, le_S_S, ex3_2_intro/
-| #G #L #K #W #V #U #i #l2 #HLK #_ #HVU *
+  #g #d1 #HW #HV #Hd1 /4 width=6 by da_ldec, lt_to_le, le_S_S, ex3_2_intro/
+| #G #L #K #W #V #U #i #d2 #HLK #_ #HVU *
   lapply (drop_fwd_drop2 … HLK)
   /4 width=10 by da_lift, da_ldec, lt_to_le, le_S_S, ex3_2_intro/
-| #a #I #G #L #V #T #U #l2 #_ * /3 width=5 by da_bind, ex3_2_intro/
-| #G #L #V #T #U #l2 #_ * /3 width=5 by da_flat, ex3_2_intro/
-| #G #L #W #T #U #l2 #_ * /3 width=5 by da_flat, ex3_2_intro/
+| #a #I #G #L #V #T #U #d2 #_ * /3 width=5 by da_bind, ex3_2_intro/
+| #G #L #V #T #U #d2 #_ * /3 width=5 by da_flat, ex3_2_intro/
+| #G #L #W #T #U #d2 #_ * /3 width=5 by da_flat, ex3_2_intro/
 ]
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lstas_inv_refl_pos: ∀h,G,L,T,l. ⦃G, L⦄ ⊢ T •*[h, l+1] T → ⊥.
-#h #G #L #T #l2 #H elim (lstas_inv_da_ge … (l2+1) H) -H
-#g #l1 #HT1 #HT12 #Hl21 lapply (da_mono … HT1 … HT12) -h -G -L -T
+lemma lstas_inv_refl_pos: ∀h,G,L,T,d. ⦃G, L⦄ ⊢ T •*[h, d+1] T → ⊥.
+#h #G #L #T #d2 #H elim (lstas_inv_da_ge … (d2+1) H) -H
+#g #d1 #HT1 #HT12 #Hd21 lapply (da_mono … HT1 … HT12) -h -G -L -T
 #H elim (discr_x_minus_xy … H) -H
 [ #H destruct /2 width=3 by le_plus_xSy_O_false/
-| -l1 <plus_n_Sm #H destruct 
+| -d1 <plus_n_Sm #H destruct 
 ]
 qed-.