milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
index 2760e2a338e72cd8d351f50e03a5780d9ea5dff4..c5ad6426a47db9cc6a83c27c86b65e5d764fd38a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
@@ -23,50 +23,50 @@ include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* Properties with unbound rt-computation on full local environments  *******)
 
-lemma lpxs_fpbs: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1, T⦄ ≥[h, o] ⦃G, L2, T⦄.
-#h #o #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
+lemma lpxs_fpbs: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1, T⦄ ≥[h] ⦃G, L2, T⦄.
+#h #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
 /3 width=5 by fpbq_lpx, fpbs_strap1/
 qed.
 
-lemma fpbs_lpxs_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ →
-                       ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
+lemma fpbs_lpxs_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L, T2⦄ →
+                       ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
+#h #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
 /3 width=5 by fpbs_strap1, fpbq_lpx/
 qed-.
 
-lemma lpxs_fpbs_trans: ∀h,o,G1,G2,L,L2,T1,T2. ⦃G1, L, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       ∀L1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
+lemma lpxs_fpbs_trans: ∀h,G1,G2,L,L2,T1,T2. ⦃G1, L, T1⦄ ≥[h] ⦃G2, L2, T2⦄ →
+                       ∀L1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
+#h #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
 /3 width=5 by fpbs_strap2, fpbq_lpx/
 qed-.
 
 (* Basic_2A1: uses: lpxs_lleq_fpbs *)
-lemma lpxs_fdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h] L →
-                      ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma lpxs_fdeq_fpbs: ∀h,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h] L →
+                      ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=3 by lpxs_fpbs_trans, fdeq_fpbs/ qed.
 
-lemma fpbs_lpx_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ →
-                      ∀L2. ⦃G2, L⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L, T2⦄ →
+                      ∀L2. ⦃G2, L⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ qed-.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma fqus_lpxs_fpbs: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L, T2⦄ →
-                      ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma fqus_lpxs_fpbs: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L, T2⦄ →
+                      ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
 
 (* Properties with unbound context-sensitive parallel rt-computation ********)
 
-lemma cpxs_fqus_lpxs_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
                            ∀G2,L,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L, T2⦄ →
-                           ∀L2.⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+                           ∀L2.⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
 /3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
 
-lemma fpbs_cpxs_tdeq_fqup_lpx_trans: ∀h,o,G1,G3,L1,L3,T1,T3. ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G3, L3, T3⦄ →
-                                     ∀T4. ⦃G3, L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛[h, o] T5 →
+lemma fpbs_cpxs_tdeq_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1, L1, T1⦄ ≥ [h] ⦃G3, L3, T3⦄ →
+                                     ∀T4. ⦃G3, L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
                                      ∀G2,L4,T2. ⦃G3, L3, T5⦄ ⊐+ ⦃G2, L4, T2⦄ →
-                                     ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
+                                     ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥ [h] ⦃G2, L2, T2⦄.
+#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
 @(fpbs_fqup_trans … H34) -G2 -L4 -T2
 /3 width=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/
@@ -75,19 +75,19 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: fpbs_intro_alt *)
-lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
+lemma fpbs_intro_star: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
                        ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
                        ∀L0. ⦃G, L⦄ ⊢ ⬈*[h] L0 →
-                       ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
+                       ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ .
 /3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_fdeq/ qed.
 
 (* Advanced inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: fpbs_inv_alt *)
-lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
+lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ →
                      ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
-                                  & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
+                                  & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛ ⦃G2, L2, T2⦄.
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
 [ /2 width=9 by ex4_5_intro/
 | #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0
   [ #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42