X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fmultiple%2Fcpys_alt.ma;h=d868ef407adb8e53e4e63abaaca6dc2f2b0e35cc;hb=c60524dec7ace912c416a90d6b926bee8553250b;hp=2d550cdbc9dd742d4e471d4a4863d7be86f59b6f;hpb=f10cfe417b6b8ec1c7ac85c6ecf5fb1b3fdf37db;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/cpys_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/cpys_alt.ma
index 2d550cdbc..d868ef407 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/cpys_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/cpys_alt.ma
@@ -19,84 +19,84 @@ include "basic_2/multiple/cpys_lift.ma".
 
 (* alternative definition of cpys *)
 inductive cpysa: ynat → ynat → relation4 genv lenv term term ≝
-| cpysa_atom : ∀I,G,L,d,e. cpysa d e G L (⓪{I}) (⓪{I})
-| cpysa_subst: ∀I,G,L,K,V1,V2,W2,i,d,e. d ≤ yinj i → i < d+e →
-               ⬇[i] L ≡ K.ⓑ{I}V1 → cpysa 0 (⫰(d+e-i)) G K V1 V2 →
-               ⬆[0, i+1] V2 ≡ W2 → cpysa d e G L (#i) W2
-| cpysa_bind : ∀a,I,G,L,V1,V2,T1,T2,d,e.
-               cpysa d e G L V1 V2 → cpysa (⫯d) e G (L.ⓑ{I}V1) T1 T2 →
-               cpysa d e G L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
-| cpysa_flat : ∀I,G,L,V1,V2,T1,T2,d,e.
-               cpysa d e G L V1 V2 → cpysa d e G L T1 T2 →
-               cpysa d e G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
+| cpysa_atom : ∀I,G,L,l,m. cpysa l m G L (⓪{I}) (⓪{I})
+| cpysa_subst: ∀I,G,L,K,V1,V2,W2,i,l,m. l ≤ yinj i → i < l+m →
+               ⬇[i] L ≡ K.ⓑ{I}V1 → cpysa 0 (⫰(l+m-i)) G K V1 V2 →
+               ⬆[0, i+1] V2 ≡ W2 → cpysa l m G L (#i) W2
+| cpysa_bind : ∀a,I,G,L,V1,V2,T1,T2,l,m.
+               cpysa l m G L V1 V2 → cpysa (⫯l) m G (L.ⓑ{I}V1) T1 T2 →
+               cpysa l m G L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
+| cpysa_flat : ∀I,G,L,V1,V2,T1,T2,l,m.
+               cpysa l m G L V1 V2 → cpysa l m G L T1 T2 →
+               cpysa l m G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
 .
 
 interpretation
    "context-sensitive extended multiple substritution (term) alternative"
-   'PSubstStarAlt G L T1 d e T2 = (cpysa d e G L T1 T2).
+   'PSubstStarAlt G L T1 l m T2 = (cpysa l m G L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma lsuby_cpysa_trans: ∀G,d,e. lsub_trans … (cpysa d e G) (lsuby d e).
-#G #d #e #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2 -d -e
+lemma lsuby_cpysa_trans: ∀G,l,m. lsub_trans … (cpysa l m G) (lsuby l m).
+#G #l #m #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2 -l -m
 [ //
-| #I #G #L1 #K1 #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
+| #I #G #L1 #K1 #V1 #V2 #W2 #i #l #m #Hli #Hilm #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
   elim (lsuby_drop_trans_be … HL12 … HLK1) -HL12 -HLK1 /3 width=7 by cpysa_subst/
 | /4 width=1 by lsuby_succ, cpysa_bind/
 | /3 width=1 by cpysa_flat/
 ]
 qed-.
 
-lemma cpysa_refl: ∀G,T,L,d,e. ⦃G, L⦄ ⊢ T ▶▶*[d, e] T.
+lemma cpysa_refl: ∀G,T,L,l,m. ⦃G, L⦄ ⊢ T ▶▶*[l, m] T.
 #G #T elim T -T //
 #I elim I -I /2 width=1 by cpysa_bind, cpysa_flat/
 qed.
 
-lemma cpysa_cpy_trans: ∀G,L,T1,T,d,e. ⦃G, L⦄ ⊢ T1 ▶▶*[d, e] T →
-                       ∀T2. ⦃G, L⦄ ⊢ T ▶[d, e] T2 → ⦃G, L⦄ ⊢ T1 ▶▶*[d, e] T2.
-#G #L #T1 #T #d #e #H elim H -G -L -T1 -T -d -e
-[ #I #G #L #d #e #X #H
+lemma cpysa_cpy_trans: ∀G,L,T1,T,l,m. ⦃G, L⦄ ⊢ T1 ▶▶*[l, m] T →
+                       ∀T2. ⦃G, L⦄ ⊢ T ▶[l, m] T2 → ⦃G, L⦄ ⊢ T1 ▶▶*[l, m] T2.
+#G #L #T1 #T #l #m #H elim H -G -L -T1 -T -l -m
+[ #I #G #L #l #m #X #H
   elim (cpy_inv_atom1 … H) -H // * /2 width=7 by cpysa_subst/
-| #I #G #L #K #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK #_ #HVW2 #IHV12 #T2 #H
+| #I #G #L #K #V1 #V2 #W2 #i #l #m #Hli #Hilm #HLK #_ #HVW2 #IHV12 #T2 #H
   lapply (drop_fwd_drop2 … HLK) #H0LK
-  lapply (cpy_weak … H 0 (d+e) ? ?) -H // #H
+  lapply (cpy_weak … H 0 (l+m) ? ?) -H // #H
   elim (cpy_inv_lift1_be … H … H0LK … HVW2) -H -H0LK -HVW2
   /3 width=7 by cpysa_subst, ylt_fwd_le_succ/
-| #a #I #G #L #V1 #V #T1 #T #d #e #_ #_ #IHV1 #IHT1 #X #H
+| #a #I #G #L #V1 #V #T1 #T #l #m #_ #_ #IHV1 #IHT1 #X #H
   elim (cpy_inv_bind1 … H) -H #V2 #T2 #HV2 #HT2 #H destruct
   /5 width=5 by cpysa_bind, lsuby_cpy_trans, lsuby_succ/
-| #I #G #L #V1 #V #T1 #T #d #e #_ #_ #IHV1 #IHT1 #X #H
+| #I #G #L #V1 #V #T1 #T #l #m #_ #_ #IHV1 #IHT1 #X #H
   elim (cpy_inv_flat1 … H) -H #V2 #T2 #HV2 #HT2 #H destruct /3 width=1 by cpysa_flat/
 ]
 qed-.
 
-lemma cpys_cpysa: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → ⦃G, L⦄ ⊢ T1 ▶▶*[d, e] T2.
+lemma cpys_cpysa: ∀G,L,T1,T2,l,m. ⦃G, L⦄ ⊢ T1 ▶*[l, m] T2 → ⦃G, L⦄ ⊢ T1 ▶▶*[l, m] T2.
 /3 width=8 by cpysa_cpy_trans, cpys_ind/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cpysa_inv_cpys: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶▶*[d, e] T2 → ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2.
-#G #L #T1 #T2 #d #e #H elim H -G -L -T1 -T2 -d -e
+lemma cpysa_inv_cpys: ∀G,L,T1,T2,l,m. ⦃G, L⦄ ⊢ T1 ▶▶*[l, m] T2 → ⦃G, L⦄ ⊢ T1 ▶*[l, m] T2.
+#G #L #T1 #T2 #l #m #H elim H -G -L -T1 -T2 -l -m
 /2 width=7 by cpys_subst, cpys_flat, cpys_bind, cpy_cpys/
 qed-.
 
 (* Advanced eliminators *****************************************************)
 
 lemma cpys_ind_alt: ∀R:ynat→ynat→relation4 genv lenv term term.
-                    (∀I,G,L,d,e. R d e G L (⓪{I}) (⓪{I})) →
-                    (∀I,G,L,K,V1,V2,W2,i,d,e. d ≤ yinj i → i < d + e →
-                     ⬇[i] L ≡ K.ⓑ{I}V1 → ⦃G, K⦄ ⊢ V1 ▶*[O, ⫰(d+e-i)] V2 →
-                     ⬆[O, i+1] V2 ≡ W2 → R O (⫰(d+e-i)) G K V1 V2 → R d e G L (#i) W2
+                    (∀I,G,L,l,m. R l m G L (⓪{I}) (⓪{I})) →
+                    (∀I,G,L,K,V1,V2,W2,i,l,m. l ≤ yinj i → i < l + m →
+                     ⬇[i] L ≡ K.ⓑ{I}V1 → ⦃G, K⦄ ⊢ V1 ▶*[O, ⫰(l+m-i)] V2 →
+                     ⬆[O, i+1] V2 ≡ W2 → R O (⫰(l+m-i)) G K V1 V2 → R l m G L (#i) W2
                     ) →
-                    (∀a,I,G,L,V1,V2,T1,T2,d,e. ⦃G, L⦄ ⊢ V1 ▶*[d, e] V2 →
-                     ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ▶*[⫯d, e] T2 → R d e G L V1 V2 →
-                     R (⫯d) e G (L.ⓑ{I}V1) T1 T2 → R d e G L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
+                    (∀a,I,G,L,V1,V2,T1,T2,l,m. ⦃G, L⦄ ⊢ V1 ▶*[l, m] V2 →
+                     ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ▶*[⫯l, m] T2 → R l m G L V1 V2 →
+                     R (⫯l) m G (L.ⓑ{I}V1) T1 T2 → R l m G L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
                     ) →
-                    (∀I,G,L,V1,V2,T1,T2,d,e. ⦃G, L⦄ ⊢ V1 ▶*[d, e] V2 →
-                     ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → R d e G L V1 V2 →
-                     R d e G L T1 T2 → R d e G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
+                    (∀I,G,L,V1,V2,T1,T2,l,m. ⦃G, L⦄ ⊢ V1 ▶*[l, m] V2 →
+                     ⦃G, L⦄ ⊢ T1 ▶*[l, m] T2 → R l m G L V1 V2 →
+                     R l m G L T1 T2 → R l m G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
                     ) →
-                    ∀d,e,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → R d e G L T1 T2.
-#R #H1 #H2 #H3 #H4 #d #e #G #L #T1 #T2 #H elim (cpys_cpysa … H) -G -L -T1 -T2 -d -e
+                    ∀l,m,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ▶*[l, m] T2 → R l m G L T1 T2.
+#R #H1 #H2 #H3 #H4 #l #m #G #L #T1 #T2 #H elim (cpys_cpysa … H) -G -L -T1 -T2 -l -m
 /3 width=8 by cpysa_inv_cpys/
 qed-.