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[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_lpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
index f5cefda3a524037cc042e8c29622feb8addd650a..dbefb4db53b75f3496b5ccdc02d42c3f8734a658 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
@@ -44,22 +44,22 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma cpx_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
-                 ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈[h] T2 →
-                 ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+lemma cpx_bind2: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
+                 ∀I,T1,T2. ⦃G,L.ⓑ{I}V2⦄ ⊢ T1 ⬈[h] T2 →
+                 ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
 /4 width=5 by lpx_cpx_trans, cpxs_bind_dx, lpx_pair/ qed.
 
-lemma cpxs_bind2_dx: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
-                     ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
-                     ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+lemma cpxs_bind2_dx: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
+                     ∀I,T1,T2. ⦃G,L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
+                     ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
 /4 width=5 by lpx_cpxs_trans, cpxs_bind_dx, lpx_pair/ qed.
 
 (* Properties with plus-iterated structural successor for closures **********)
 
 (* Basic_2A1: uses: lpx_fqup_trans *)
-lemma lpx_fqup_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                      ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h] L1 →
-                      ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, K1, T⦄ ⊐+[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h] L2.
+lemma lpx_fqup_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄ →
+                      ∀K1. ⦃G1,K1⦄ ⊢ ⬈[h] L1 →
+                      ∃∃K2,T. ⦃G1,K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1,K1,T⦄ ⊐+[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ⬈[h] L2.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 [ #G2 #L2 #T2 #H12 #K1 #HKL1 elim (lpx_fqu_trans … H12 … HKL1) -L1
   /3 width=5 by cpx_cpxs, fqu_fqup, ex3_2_intro/
@@ -73,9 +73,9 @@ qed-.
 (* Properties with star-iterated structural successor for closures **********)
 
 (* Basic_2A1: uses: lpx_fqus_trans *)
-lemma lpx_fqus_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                      ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h] L1 →
-                      ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, K1, T⦄ ⊐*[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h] L2.
+lemma lpx_fqus_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐*[b] ⦃G2,L2,T2⦄ →
+                      ∀K1. ⦃G1,K1⦄ ⊢ ⬈[h] L1 →
+                      ∃∃K2,T. ⦃G1,K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1,K1,T⦄ ⊐*[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ⬈[h] L2.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 elim (fqus_inv_fqup … H) -H
 [ #H12 elim (lpx_fqup_trans … H12 … HKL1) -L1 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/