milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
index 4f23c0d0095759e30b7fe22eebf212f8bc76d6d8..09a7919b1901bdd33371e42070f1549a9af3c960 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
@@ -19,40 +19,40 @@ include "basic_2/rt_computation/fpbs_fqup.ma".
 
 (* Properties with unbound context-sensitive parallel rt-computation ********)
 
-lemma cpxs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-#h #o #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
+lemma cpxs_fpbs: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h] ⦃G, L, T2⦄.
+#h #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=5 by fpbq_cpx, fpbs_strap1/
 qed.
 
-lemma fpbs_cpxs_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       ∀T2. ⦃G, L⦄ ⊢ T ⬈*[h] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-#h #o #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
+lemma fpbs_cpxs_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h] ⦃G, L, T⦄ →
+                       ∀T2. ⦃G, L⦄ ⊢ T ⬈*[h] T2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G, L, T2⦄.
+#h #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=5 by fpbs_strap1, fpbq_cpx/
 qed-.
 
-lemma cpxs_fpbs_trans: ∀h,o,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       ∀T1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
+lemma cpxs_fpbs_trans: ∀h,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h] ⦃G2, L2, T2⦄ →
+                       ∀T1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
+#h #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
 /3 width=5 by fpbs_strap2, fpbq_cpx/
 qed-.
 
-lemma cpxs_tdeq_fpbs_trans: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                            ∀T0. T ≛[h, o] T0 →
-                            ∀G2,L2,T2. ⦃G1, L1, T0⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma cpxs_tdeq_fpbs_trans: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+                            ∀T0. T ≛ T0 →
+                            ∀G2,L2,T2. ⦃G1, L1, T0⦄ ≥[h] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=3 by cpxs_fpbs_trans, tdeq_fpbs_trans/ qed-.
 
-lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
-                      ∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
+lemma cpxs_tdeq_fpbs: ∀h,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
+                      ∀T2. T ≛ T2 → ⦃G, L, T1⦄ ≥[h] ⦃G, L, T2⦄.
 /4 width=3 by cpxs_fpbs_trans, fdeq_fpbs, tdeq_fdeq/ qed.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma cpxs_fqus_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma cpxs_fqus_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
 
 (* Properties with plus-iterated structural successor for closures **********)
 
-lemma cpxs_fqup_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma cpxs_fqup_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.