- some renaming according to the written version of basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
index 034024b72ea8708b9ac9de822ca16618db0853b3..05fc77f90524f0e23e52c4732c495b5a4b5ea4f3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
@@ -20,44 +20,44 @@ include "basic_2/computation/lsx.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma lsx_lleq_trans: ∀h,g,T,G,L1,d. G ⊢ ⬊*[h, g, T, d] L1 →
-                      ∀L2. L1 ≡[T, d] L2 → G ⊢ ⬊*[h, g, T, d] L2.
-#h #g #T #G #L1 #d #H @(lsx_ind … H) -L1
+lemma lsx_lleq_trans: ∀h,g,T,G,L1,l. G ⊢ ⬊*[h, g, T, l] L1 →
+                      ∀L2. L1 ≡[T, l] L2 → G ⊢ ⬊*[h, g, T, l] L2.
+#h #g #T #G #L1 #l #H @(lsx_ind … H) -L1
 #L1 #_ #IHL1 #L2 #HL12 @lsx_intro
 #K2 #HLK2 #HnLK2 elim (lleq_lpx_trans … HLK2 … HL12) -HLK2
 /5 width=4 by lleq_canc_sn, lleq_trans/
 qed-.
 
-lemma lsx_lpx_trans: ∀h,g,T,G,L1,d. G ⊢ ⬊*[h, g, T, d] L1 →
-                     ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → G ⊢ ⬊*[h, g, T, d] L2.
-#h #g #T #G #L1 #d #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (lleq_dec T L1 L2 d) /3 width=4 by lsx_lleq_trans/
+lemma lsx_lpx_trans: ∀h,g,T,G,L1,l. G ⊢ ⬊*[h, g, T, l] L1 →
+                     ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → G ⊢ ⬊*[h, g, T, l] L2.
+#h #g #T #G #L1 #l #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
+elim (lleq_dec T L1 L2 l) /3 width=4 by lsx_lleq_trans/
 qed-.
 
-lemma lsx_leq_conf: ∀h,g,G,L1,T,d. G ⊢ ⬊*[h, g, T, d] L1 →
-                    ∀L2. L1 ⩬[d, ∞] L2 → G ⊢ ⬊*[h, g, T, d] L2.
-#h #g #G #L1 #T #d #H @(lsx_ind … H) -L1
+lemma lsx_lreq_conf: ∀h,g,G,L1,T,l. G ⊢ ⬊*[h, g, T, l] L1 →
+                    ∀L2. L1 ⩬[l, ∞] L2 → G ⊢ ⬊*[h, g, T, l] L2.
+#h #g #G #L1 #T #l #H @(lsx_ind … H) -L1
 #L1 #_ #IHL1 #L2 #HL12 @lsx_intro
-#L3 #HL23 #HnL23 elim (leq_lpx_trans_lleq … HL12 … HL23) -HL12 -HL23
+#L3 #HL23 #HnL23 elim (lreq_lpx_trans_lleq … HL12 … HL23) -HL12 -HL23
 #L0 #HL03 #HL10 #H elim (H T) -H /4 width=4 by/
 qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma lsx_fwd_bind_dx: ∀h,g,a,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L →
-                       G ⊢ ⬊*[h, g, T, ⫯d] L.ⓑ{I}V.
-#h #g #a #I #G #L #V1 #T #d #H @(lsx_ind … H) -L
+lemma lsx_fwd_bind_dx: ∀h,g,a,I,G,L,V,T,l. G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L →
+                       G ⊢ ⬊*[h, g, T, ⫯l] L.ⓑ{I}V.
+#h #g #a #I #G #L #V1 #T #l #H @(lsx_ind … H) -L
 #L1 #_ #IHL1 @lsx_intro
 #Y #H #HT elim (lpx_inv_pair1 … H) -H
 #L2 #V2 #HL12 #_ #H destruct
-@(lsx_leq_conf … (L2.ⓑ{I}V1)) /2 width=1 by leq_succ/
+@(lsx_lreq_conf … (L2.ⓑ{I}V1)) /2 width=1 by lreq_succ/
 @IHL1 // #H @HT -IHL1 -HL12 -HT
-@(lleq_leq_trans … (L2.ⓑ{I}V1))
-/2 width=2 by lleq_fwd_bind_dx, leq_succ/
+@(lleq_lreq_trans … (L2.ⓑ{I}V1))
+/2 width=2 by lleq_fwd_bind_dx, lreq_succ/
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lsx_inv_bind: ∀h,g,a,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓑ{a, I}V.T, d] L →
-                    G ⊢ ⬊*[h, g, V, d] L ∧ G ⊢ ⬊*[h, g, T, ⫯d] L.ⓑ{I}V.
+lemma lsx_inv_bind: ∀h,g,a,I,G,L,V,T,l. G ⊢ ⬊*[h, g, ⓑ{a, I}V.T, l] L →
+                    G ⊢ ⬊*[h, g, V, l] L ∧ G ⊢ ⬊*[h, g, T, ⫯l] L.ⓑ{I}V.
 /3 width=4 by lsx_fwd_bind_sn, lsx_fwd_bind_dx, conj/ qed-.