- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / llpx / cpxs_llpx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/cpxs_llpx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/cpxs_llpx.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/cpxs_llpx.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/llpx_ldrop.ma".
+include "basic_2/computation/cpxs_cpxs.ma".
+
+(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
+
+(* Properties on lazy sn reduction on local environments ********************)
+
+lemma cpxs_llpx_conf: ∀h,g,G. s_r_confluent1 … (cpxs h g G) (llpx h g G 0).
+/3 width=5 by llpx_cpx_conf, s_r_conf1_LTC1/ qed-.
+
+lemma llpx_cpx_trans: ∀h,g,G. s_r_transitive … (cpx h g G) (llpx h g G 0).
+#h #g #G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
+[ /2 width=3 by/
+| /3 width=2 by cpx_cpxs, cpx_sort/
+| #I #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
+  elim (llpx_inv_lref_ge_dx … HL12 … HLK2) -L2
+  /5 width=8 by cpxs_delta, cpxs_strap2, llpx_cpx_conf/
+| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
+  elim (llpx_inv_bind_O … HL12) -HL12 /4 width=1 by cpxs_bind/
+| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
+  elim (llpx_inv_flat … HL12) -HL12 /3 width=1 by cpxs_flat/
+| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12
+  elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_zeta/
+| #G #L2 #V2 #T1 #T2 #HT12 #IHT12 #L1 #HL12
+  elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_tau/
+| #G #L2 #V1 #V2 #T2 #HV12 #IHV12 #L1 #HL12
+  elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_ti/
+| #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12
+  elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
+  elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_beta/
+| #a #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12
+  elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
+  elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_theta/
+]
+qed-.
+
+lemma llpx_cpxs_trans: ∀h,g,G. s_rs_transitive … (cpx h g G) (llpx h g G 0).
+#h #g #G @s_r_trans_LTC1 /2 width=3 by llpx_cpx_trans, llpx_cpx_conf/ (**) (* full auto fails here but works in cprs_cprs *)
+qed-.