milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / fpn / fpn_fpn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpn_fpn.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpn_fpn.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpn_fpn.etc
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/reduction/lpx_lpx.ma".
+include "basic_2/reduction/fpn.ma".
+
+(* REDUCTION FOR "BIG TREE" NORMAL FORMS ************************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fpn_fqu_trans: ∀h,g,F1,G1,K1,L1,V1,T1. ⦃F1, K1, V1⦄ ⊢ ⋕➡[h, g] ⦃G1, L1, T1⦄ →
+                     ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                     ∃∃F2,K2,V2. ⦃F1, K1, V1⦄ ⊃ ⦃F2, K2, V2⦄ & ⦃F2, K2, V2⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄.
+#h #g #F1 #G1 #K1 #L1 #V1 #T1 * -G1 -L1 -T1
+#L1 #HKL1 #HV1 #G2 #L2 #T2 #H12 elim (lpx_lleq_fqu_trans … H12 … HKL1 HV1) -L1
+/3 width=5 by fpn_intro, ex2_3_intro/
+qed-.
+
+lemma fpn_fquq_trans: ∀h,g,F1,G1,K1,L1,V1,T1. ⦃F1, K1, V1⦄ ⊢ ⋕➡[h, g] ⦃G1, L1, T1⦄ →
+                      ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                      ∃∃F2,K2,V2. ⦃F1, K1, V1⦄ ⊃⸮ ⦃F2, K2, V2⦄ & ⦃F2, K2, V2⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄.
+#h #g #F1 #G1 #K1 #L1 #V1 #T1 * -G1 -L1 -T1
+#L1 #HKL1 #HV1 #G2 #L2 #T2 #H12 elim (lpx_lleq_fquq_trans … H12 … HKL1 HV1) -L1
+/3 width=5 by fpn_intro, ex2_3_intro/
+qed-.
+
+lemma fpn_fqup_trans: ∀h,g,F1,G1,K1,L1,V1,T1. ⦃F1, K1, V1⦄ ⊢ ⋕➡[h, g] ⦃G1, L1, T1⦄ →
+                      ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                      ∃∃F2,K2,V2. ⦃F1, K1, V1⦄ ⊃+ ⦃F2, K2, V2⦄ & ⦃F2, K2, V2⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄.
+#h #g #F1 #G1 #K1 #L1 #V1 #T1 * -G1 -L1 -T1
+#L1 #HKL1 #HV1 #G2 #L2 #T2 #H12 elim (lpx_lleq_fqup_trans … H12 … HKL1 HV1) -L1
+/3 width=5 by fpn_intro, ex2_3_intro/
+qed-.
+
+lemma fpn_fqus_trans: ∀h,g,F1,G1,K1,L1,V1,T1. ⦃F1, K1, V1⦄ ⊢ ⋕➡[h, g] ⦃G1, L1, T1⦄ →
+                      ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                      ∃∃F2,K2,V2. ⦃F1, K1, V1⦄ ⊃* ⦃F2, K2, V2⦄ & ⦃F2, K2, V2⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄.
+#h #g #F1 #G1 #K1 #L1 #V1 #T1 * -G1 -L1 -T1
+#L1 #HKL1 #HV1 #G2 #L2 #T2 #H12 elim (lpx_lleq_fqus_trans … H12 … HKL1 HV1) -L1
+/3 width=5 by fpn_intro, ex2_3_intro/
+qed-.