- some renaming according to the written version of basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
index 0accd974f7751d572c73535c06fe5566d56f5bc8..d84202bbc7a60815b7533b9a6b27c6b1f7507992 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
@@ -19,16 +19,16 @@ include "basic_2/computation/lsx_alt.ma".
 
 (* Advanced properties ******************************************************)
 
-fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 →
-                        ∀Y,T. G ⊢ ⬊*[h, g, T, ⫯d] Y →
+fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
+                        ∀Y,T. G ⊢ ⬊*[h, g, T, ⫯l] Y →
                         ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
-                        G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L2.
-#h #g #a #I #G #L1 #V #d #H @(lsx_ind_alt … H) -L1
+                        G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L2.
+#h #g #a #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
 #L1 #HL1 #IHL1 #Y #T #H @(lsx_ind_alt … H) -Y
 #Y #HY #IHY #L2 #H #HL12 destruct @lsx_intro_alt
 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
 #HL10 #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ]
-[ #HnV elim (lleq_dec V L1 L2 d)
+[ #HnV elim (lleq_dec V L1 L2 l)
   [ #HV @(IHL1 … L0) /3 width=5 by lsx_lpxs_trans, lpxs_pair, lleq_canc_sn/ (**) (* full auto too slow *)
   | -HnV -HL10 /4 width=5 by lsx_lpxs_trans, lpxs_pair/
   ]
@@ -36,20 +36,20 @@ fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 →
 ]
 qed-.
 
-lemma lsx_bind: ∀h,g,a,I,G,L,V,d. G ⊢ ⬊*[h, g, V, d] L →
-                ∀T. G ⊢ ⬊*[h, g, T, ⫯d] L.ⓑ{I}V →
-                G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L.
+lemma lsx_bind: ∀h,g,a,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
+                ∀T. G ⊢ ⬊*[h, g, T, ⫯l] L.ⓑ{I}V →
+                G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L.
 /2 width=3 by lsx_bind_lpxs_aux/ qed.
 
-lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 →
-                     ∀L2,T. G ⊢ ⬊*[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
-                     G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L2.
-#h #g #I #G #L1 #V #d #H @(lsx_ind_alt … H) -L1
+lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
+                     ∀L2,T. G ⊢ ⬊*[h, g, T, l] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
+                     G ⊢ ⬊*[h, g, ⓕ{I}V.T, l] L2.
+#h #g #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
 #L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind_alt … H) -L2
 #L2 #HL2 #IHL2 #HL12 @lsx_intro_alt
 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
 #HL10 #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
-[ #HnV elim (lleq_dec V L1 L2 d)
+[ #HnV elim (lleq_dec V L1 L2 l)
   [ #HV @(IHL1 … L0) /3 width=3 by lsx_lpxs_trans, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
   | -HnV -HL10 /3 width=4 by lsx_lpxs_trans/
   ]
@@ -57,6 +57,6 @@ lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⬊*[h, g, V, d] L1 →
 ]
 qed-.
 
-lemma lsx_flat: ∀h,g,I,G,L,V,d. G ⊢ ⬊*[h, g, V, d] L →
-                ∀T. G ⊢ ⬊*[h, g, T, d] L → G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L.
+lemma lsx_flat: ∀h,g,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
+                ∀T. G ⊢ ⬊*[h, g, T, l] L → G ⊢ ⬊*[h, g, ⓕ{I}V.T, l] L.
 /2 width=3 by lsx_flat_lpxs/ qed.