- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsx_drop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_drop.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_drop.ma
index 664ff62a8114026a136a2dea5f90848a40a85ffb..f1a4c7b64e8f4ed33d7eb8487a08a7552a577aa4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_drop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_drop.ma
@@ -20,27 +20,27 @@ include "basic_2/computation/lsx.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma lsx_lref_free: ∀h,g,G,L,d,i. |L| ≤ i → G ⊢ ⬊*[h, g, #i, d] L.
-#h #g #G #L1 #d #i #HL1 @lsx_intro
+lemma lsx_lref_free: ∀h,g,G,L,l,i. |L| ≤ i → G ⊢ ⬊*[h, g, #i, l] L.
+#h #g #G #L1 #l #i #HL1 @lsx_intro
 #L2 #HL12 #H elim H -H
 /4 width=6 by lpx_fwd_length, lleq_free, le_repl_sn_conf_aux/
 qed.
 
-lemma lsx_lref_skip: ∀h,g,G,L,d,i. yinj i < d → G ⊢ ⬊*[h, g, #i, d] L.
-#h #g #G #L1 #d #i #HL1 @lsx_intro
+lemma lsx_lref_skip: ∀h,g,G,L,l,i. yinj i < l → G ⊢ ⬊*[h, g, #i, l] L.
+#h #g #G #L1 #l #i #HL1 @lsx_intro
 #L2 #HL12 #H elim H -H
 /3 width=4 by lpx_fwd_length, lleq_skip/
 qed.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma lsx_fwd_lref_be: ∀h,g,I,G,L,d,i. d ≤ yinj i → G ⊢ ⬊*[h, g, #i, d] L →
+lemma lsx_fwd_lref_be: ∀h,g,I,G,L,l,i. l ≤ yinj i → G ⊢ ⬊*[h, g, #i, l] L →
                        ∀K,V. ⬇[i] L ≡ K.ⓑ{I}V → G ⊢ ⬊*[h, g, V, 0] K.
-#h #g #I #G #L #d #i #Hdi #H @(lsx_ind … H) -L
+#h #g #I #G #L #l #i #Hli #H @(lsx_ind … H) -L
 #L1 #_ #IHL1 #K1 #V #HLK1 @lsx_intro
 #K2 #HK12 #HnK12 lapply (drop_fwd_drop2 … HLK1)
 #H2LK1 elim (drop_lpx_trans … H2LK1 … HK12) -H2LK1 -HK12
-#L2 #HL12 #H2LK2 #H elim (leq_drop_conf_be … H … HLK1) -H /2 width=1 by ylt_inj/
+#L2 #HL12 #H2LK2 #H elim (lreq_drop_conf_be … H … HLK1) -H /2 width=1 by ylt_inj/
 #Y #_ #HLK2 lapply (drop_fwd_drop2 … HLK2)
 #HY lapply (drop_mono … HY … H2LK2) -HY -H2LK2 #H destruct
 /4 width=10 by lleq_inv_lref_ge/
@@ -48,19 +48,19 @@ qed-.
 
 (* Properties on relocation *************************************************)
 
-lemma lsx_lift_le: ∀h,g,G,K,T,U,dt,d,e. dt ≤ yinj d →
-                   ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, T, dt] K →
-                   ∀L. ⬇[Ⓕ, d, e] L ≡ K → G ⊢ ⬊*[h, g, U, dt] L.
-#h #g #G #K #T #U #dt #d #e #Hdtd #HTU #H @(lsx_ind … H) -K
+lemma lsx_lift_le: ∀h,g,G,K,T,U,lt,l,m. lt ≤ yinj l →
+                   ⬆[l, m] T ≡ U → G ⊢ ⬊*[h, g, T, lt] K →
+                   ∀L. ⬇[Ⓕ, l, m] L ≡ K → G ⊢ ⬊*[h, g, U, lt] L.
+#h #g #G #K #T #U #lt #l #m #Hltl #HTU #H @(lsx_ind … H) -K
 #K1 #_ #IHK1 #L1 #HLK1 @lsx_intro
 #L2 #HL12 #HnU elim (lpx_drop_conf … HLK1 … HL12) -HL12
 /4 width=10 by lleq_lift_le/
 qed-.
 
-lemma lsx_lift_ge: ∀h,g,G,K,T,U,dt,d,e. yinj d ≤ dt →
-                   ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, T, dt] K →
-                   ∀L. ⬇[Ⓕ, d, e] L ≡ K → G ⊢ ⬊*[h, g, U, dt + e] L.
-#h #g #G #K #T #U #dt #d #e #Hddt #HTU #H @(lsx_ind … H) -K
+lemma lsx_lift_ge: ∀h,g,G,K,T,U,lt,l,m. yinj l ≤ lt →
+                   ⬆[l, m] T ≡ U → G ⊢ ⬊*[h, g, T, lt] K →
+                   ∀L. ⬇[Ⓕ, l, m] L ≡ K → G ⊢ ⬊*[h, g, U, lt + m] L.
+#h #g #G #K #T #U #lt #l #m #Hllt #HTU #H @(lsx_ind … H) -K
 #K1 #_ #IHK1 #L1 #HLK1 @lsx_intro
 #L2 #HL12 #HnU elim (lpx_drop_conf … HLK1 … HL12) -HL12
 /4 width=9 by lleq_lift_ge/
@@ -68,28 +68,28 @@ qed-.
 
 (* Inversion lemmas on relocation *******************************************)
 
-lemma lsx_inv_lift_le: ∀h,g,G,L,T,U,dt,d,e. dt ≤ yinj d →
-                       ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, U, dt] L →
-                       ∀K. ⬇[Ⓕ, d, e] L ≡ K → G ⊢ ⬊*[h, g, T, dt] K.
-#h #g #G #L #T #U #dt #d #e #Hdtd #HTU #H @(lsx_ind … H) -L
+lemma lsx_inv_lift_le: ∀h,g,G,L,T,U,lt,l,m. lt ≤ yinj l →
+                       ⬆[l, m] T ≡ U → G ⊢ ⬊*[h, g, U, lt] L →
+                       ∀K. ⬇[Ⓕ, l, m] L ≡ K → G ⊢ ⬊*[h, g, T, lt] K.
+#h #g #G #L #T #U #lt #l #m #Hltl #HTU #H @(lsx_ind … H) -L
 #L1 #_ #IHL1 #K1 #HLK1 @lsx_intro
 #K2 #HK12 #HnT elim (drop_lpx_trans … HLK1 … HK12) -HK12
 /4 width=10 by lleq_inv_lift_le/
 qed-.
 
-lemma lsx_inv_lift_be: ∀h,g,G,L,T,U,dt,d,e. yinj d ≤ dt → dt ≤ d + e →
-                       ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, U, dt] L →
-                       ∀K. ⬇[Ⓕ, d, e] L ≡ K → G ⊢ ⬊*[h, g, T, d] K.
-#h #g #G #L #T #U #dt #d #e #Hddt #Hdtde #HTU #H @(lsx_ind … H) -L
+lemma lsx_inv_lift_be: ∀h,g,G,L,T,U,lt,l,m. yinj l ≤ lt → lt ≤ l + m →
+                       ⬆[l, m] T ≡ U → G ⊢ ⬊*[h, g, U, lt] L →
+                       ∀K. ⬇[Ⓕ, l, m] L ≡ K → G ⊢ ⬊*[h, g, T, l] K.
+#h #g #G #L #T #U #lt #l #m #Hllt #Hltlm #HTU #H @(lsx_ind … H) -L
 #L1 #_ #IHL1 #K1 #HLK1 @lsx_intro
 #K2 #HK12 #HnT elim (drop_lpx_trans … HLK1 … HK12) -HK12
 /4 width=11 by lleq_inv_lift_be/
 qed-.
 
-lemma lsx_inv_lift_ge: ∀h,g,G,L,T,U,dt,d,e. yinj d + yinj e ≤ dt →
-                       ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, U, dt] L →
-                       ∀K. ⬇[Ⓕ, d, e] L ≡ K → G ⊢ ⬊*[h, g, T, dt-e] K.
-#h #g #G #L #T #U #dt #d #e #Hdedt #HTU #H @(lsx_ind … H) -L
+lemma lsx_inv_lift_ge: ∀h,g,G,L,T,U,lt,l,m. yinj l + yinj m ≤ lt →
+                       ⬆[l, m] T ≡ U → G ⊢ ⬊*[h, g, U, lt] L →
+                       ∀K. ⬇[Ⓕ, l, m] L ≡ K → G ⊢ ⬊*[h, g, T, lt-m] K.
+#h #g #G #L #T #U #lt #l #m #Hlmlt #HTU #H @(lsx_ind … H) -L
 #L1 #_ #IHL1 #K1 #HLK1 @lsx_intro
 #K2 #HK12 #HnT elim (drop_lpx_trans … HLK1 … HK12) -HK12
 /4 width=9 by lleq_inv_lift_ge/