- commit of the "s_computation" component ...

[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 05fc77f90524f0e23e52c4732c495b5a4b5ea4f3..81dc6e73dd273df2505eb90bb8afd55650c2ddb8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
@@ -20,23 +20,23 @@ include "basic_2/computation/lsx.ma".
 
 (* Advanced properties ******************************************************)
 
-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
+lemma lsx_lleq_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊*[h, o, T, l] L1 →
+                      ∀L2. L1 ≡[T, l] L2 → G ⊢ ⬊*[h, o, T, l] L2.
+#h #o #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,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
+lemma lsx_lpx_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊*[h, o, T, l] L1 →
+                     ∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → G ⊢ ⬊*[h, o, T, l] L2.
+#h #o #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_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
+lemma lsx_lreq_conf: ∀h,o,G,L1,T,l. G ⊢ ⬊*[h, o, T, l] L1 →
+                    ∀L2. L1 ⩬[l, ∞] L2 → G ⊢ ⬊*[h, o, T, l] L2.
+#h #o #G #L1 #T #l #H @(lsx_ind … H) -L1
 #L1 #_ #IHL1 #L2 #HL12 @lsx_intro
 #L3 #HL23 #HnL23 elim (lreq_lpx_trans_lleq … HL12 … HL23) -HL12 -HL23
 #L0 #HL03 #HL10 #H elim (H T) -H /4 width=4 by/
@@ -44,9 +44,9 @@ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-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
+lemma lsx_fwd_bind_dx: ∀h,o,a,I,G,L,V,T,l. G ⊢ ⬊*[h, o, ⓑ{a,I}V.T, l] L →
+                       G ⊢ ⬊*[h, o, T, ⫯l] L.ⓑ{I}V.
+#h #o #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
@@ -58,6 +58,6 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-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.
+lemma lsx_inv_bind: ∀h,o,a,I,G,L,V,T,l. G ⊢ ⬊*[h, o, ⓑ{a, I}V.T, l] L →
+                    G ⊢ ⬊*[h, o, V, l] L ∧ G ⊢ ⬊*[h, o, T, ⫯l] L.ⓑ{I}V.
 /3 width=4 by lsx_fwd_bind_sn, lsx_fwd_bind_dx, conj/ qed-.