- some work on extensions:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / lpx_sn / lpx_lleq.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lpx_sn/lpx_lleq.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lpx_sn/lpx_lleq.etc
deleted file mode 100644 (file)
index 353f810..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/lpx_sn/lpx_lleq.etc
+++ /dev/null
@@ -1,108 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/relocation/lleq_ldrop.ma".
-include "basic_2/reduction/lpx_ldrop.ma".
-
-(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
-
-(* Properties on lazy equivalence for local environments ********************)
-(*
-lamma pippo: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡[h, g] K2 → ∀L1. |L1| = |L2| →
-             ∃∃K1. ⦃G, L1⦄ ⊢ ➡[h, g] K1 & |K1| = |K2| &
-                   (∀T,d. L1 ⋕[T, d] L2 ↔ K1 ⋕[T, d] K2).
-#h #g #G #L2 #K2 #H elim H -L2 -K2
-[ #L1 #H >(length_inv_zero_dx … H) -L1 /3 width=5 by ex3_intro, conj/
-| #I2 #L2 #K2 #V2 #W2 #_ #HVW2 #IHLK2 #Y #H
-  elim (length_inv_pos_dx … H) -H #I #L1 #V1 #HL12 #H destruct
-  elim (IHLK2 … HL12) -IHLK2 #K1 #HLK1 #HK12 #IH
-  elim (eq_term_dec V1 V2) #H destruct
-  [ @(ex3_intro … (K1.ⓑ{I}W2)) normalize /2 width=1 by /
-*)
-axiom lleq_lpx_trans: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡[h, g] K2 →
-                      ∀L1,T,d. L1 ⋕[T, d] L2 →
-                      ∃∃K1. ⦃G, L1⦄ ⊢ ➡[h, g] K1 & K1 ⋕[T, d] K2.
-(*
-#h #g #G #L2 #K2 #H elim H -L2 -K2
-[ #L1 #T #d #H lapply (lleq_fwd_length … H) -H
-  #H >(length_inv_zero_dx … H) -L1 /2 width=3 by ex2_intro/
-| #I2 #L2 #K2 #V2 #W2 #HLK2 #HVW2 #IHLK2 #Y #T #d #HT
-  lapply (lleq_fwd_length … HT) #H
-  elim (length_inv_pos_dx … H) -H #I1 #L1 #V1 #HL12 #H destruct
-  elim (eq_term_dec V1 V2) #H destruct
-  [ @ex2_intro …
-*)
-
-lemma lpx_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                          ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
-                          ∃∃K2. ⦃G1, K1, T1⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-[ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpx_inv_pair2 … H1) -H1
-  #K0 #V0 #H1KL1 #_ #H destruct
-  elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 //
-  #K1 #H #H2KL1 lapply (ldrop_inv_O2 … H) -H #H destruct
-  /2 width=4 by fqu_lref_O, ex3_intro/
-| * [ #a ] #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H
-  [ elim (lleq_inv_bind … H)
-  | elim (lleq_inv_flat … H)
-  ] -H /2 width=4 by fqu_pair_sn, ex3_intro/
-| #a #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_bind_O … H) -H
-  /3 width=4 by lpx_pair, fqu_bind_dx, ex3_intro/
-| #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_flat … H) -H
-  /2 width=4 by fqu_flat_dx, ex3_intro/
-| #G1 #L1 #L #T1 #U1 #e #HL1 #HTU1 #K1 #H1KL1 #H2KL1
-  elim (ldrop_O1_le (e+1) K1)
-  [ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 //
-    #H2KL elim (lpx_ldrop_trans_O1 … H1KL1 … HL1) -L1
-    #K0 #HK10 #H1KL lapply (ldrop_mono … HK10 … HK1) -HK10 #H destruct
-    /3 width=4 by fqu_drop, ex3_intro/
-  | lapply (ldrop_fwd_length_le2 … HL1) -L -T1 -g
-    lapply (lleq_fwd_length … H2KL1) //
-  ]
-]
-qed-.
-
-lemma lpx_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
-elim (fquq_inv_gen … H) -H
-[ #H elim (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
-  /3 width=4 by fqu_fquq, ex3_intro/
-| * #HG #HL #HT destruct /2 width=4 by ex3_intro/
-]
-qed-.
-
-lemma lpx_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
-[ #G2 #L2 #T2 #H #K1 #H1KL1 #H2KL1 elim (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
-  /3 width=4 by fqu_fqup, ex3_intro/
-| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #K1 #H1KL1 #H2KL1 elim (IHT1 … H2KL1) // -L1
-  #K #HT1 #H1KL #H2KL elim (lpx_lleq_fqu_trans … HT2 … H1KL H2KL) -L
-  /3 width=5 by fqup_strap1, ex3_intro/
-]
-qed-.
-
-lemma lpx_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
-elim (fqus_inv_gen … H) -H
-[ #H elim (lpx_lleq_fqup_trans … H … H1KL1 H2KL1) -L1
-  /3 width=4 by fqup_fqus, ex3_intro/
-| * #HG #HL #HT destruct /2 width=4 by ex3_intro/
-]
-qed-.