From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Mon, 2 Dec 2013 19:19:25 +0000 (+0000)
Subject: - last patrtial commit of the "reduction" and "computation" components
X-Git-Tag: make_still_working~1032
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=1cc9a122e904468085545bb53543cc1a0f2f48f5;p=helm.git

- last patrtial commit of the "reduction" and "computation" components
- we generalized a lemma
---

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
index 3fe57b92a..beb022541 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
@@ -19,7 +19,7 @@ include "basic_2/computation/lpxs.ma".
 (* PARALLEL COMPUTATION FOR "BIG TREE" NORMAL FORMS *************************)
 
 inductive fpns (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
-| fpns_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → L1 ⋕[T] L2 → fpns h g G L1 T G L2 T
+| fpns_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → L1 ⋕[0, T] L2 → fpns h g G L1 T G L2 T
 .
 
 interpretation
@@ -34,6 +34,6 @@ lemma fpns_refl: ∀h,g. tri_reflexive … (fpns h g).
 (* Basic inversion lemmas ***************************************************) 
 
 lemma fpns_inv_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ →
-                    ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 & L1 ⋕[T1] L2 & T1 = T2.
+                    ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 & L1 ⋕[0, T1] L2 & T1 = T2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
 qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/leq.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/leq.ma
index 32924d1c2..095e1ced3 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/leq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/leq.ma
@@ -44,6 +44,15 @@ lemma leq_sym: ∀L1,L2,d,e. L1 ≃[d, e] L2 → L2 ≃[d, e] L1.
 /2 width=1 by leq_atom, leq_zero, leq_pair, leq_succ/
 qed-.
 
+lemma leq_O_Y: ∀L1,L2. |L1| = |L2| → L1 ≃[0, ∞] L2.
+#L1 elim L1 -L1
+[ #X #H lapply (length_inv_zero_sn … H) -H //
+| #L1 #I1 #V1 #IHL1 #X #H elim (length_inv_pos_sn … H) -H
+  #L2 #I2 #V2 #HL12 #H destruct
+  @(leq_pair … (∞)) /2 width=1 by/ (**) (* explicit constructor *)
+]
+qed.
+
 (* Basic forward lemmas *****************************************************)
 
 lemma leq_fwd_length: ∀L1,L2,d,e. L1 ≃[d, e] L2 → |L1| = |L2|.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
index 4b0257e6f..dc5466d62 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/relocation/ldrop_leq.ma".
 include "basic_2/relocation/lleq_lleq.ma".
 include "basic_2/reduction/cpx.ma".
 
@@ -19,24 +20,34 @@ include "basic_2/reduction/cpx.ma".
 
 (* Properties on lazy equivalence for local environments ********************)
 
-lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
-                      ∀L1. L1 ⋕[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
+lemma lleq_cpx_trans_leq: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                          ∀L1,d. L1 ⋕[d, T1] L2 → L1 ≃[d, ∞] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
 #h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_sort/
-[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_inv_lref_ge_dx … H … HLK2) -L2
-  /3 width=7 by cpx_delta/
-| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
-  /3 width=1 by cpx_bind/
-| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
-  /3 width=1 by cpx_flat/
-| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #H elim (lleq_inv_bind_O … H) -H
-  /3 width=3 by cpx_zeta/
-| #G #L2 #W1 #T1 #T2 #_ #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
-  /3 width=1 by cpx_tau/
-| #G #L2 #W1 #W2 #T1 #_ #IHW12 #L1 #H elim (lleq_inv_flat … H) -H
-  /3 width=1 by cpx_ti/
-| #a #G #L1 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
-  #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=1 by cpx_beta/
-| #a #G #L1 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
-  #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=3 by cpx_theta/
+[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #d #H #HL12 elim (lleq_inv_lref_dx … H … HLK2) -H *
+  [ #K1 #HLK1 #HV1 #Hdi elim (ldrop_leq_conf_be … HL12 … HLK1) -HL12 /2 width=1 by yle_inj/
+    >yminus_Y_inj #J #Y #X #HK12 #H lapply (ldrop_mono … H … HLK2) -L2
+    #H destruct /3 width=7 by cpx_delta/
+  | #J #K1 #V #HLK1 #_ #HV1 #Hid elim (ldrop_leq_conf_lt … HL12 … HLK1) -HL12 /2 width=1 by ylt_inj/
+    #Y #HK12 #H lapply (ldrop_mono … H … HLK2) -L2
+    #H destruct /3 width=7 by cpx_delta/
+  ]
+| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #H elim (lleq_inv_bind … H) -H
+  /4 width=3 by cpx_bind, leq_succ/
+| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
+  /3 width=3 by cpx_flat/
+| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #d #H elim (lleq_inv_bind … H) -H
+  /4 width=3 by cpx_zeta, leq_succ/
+| #G #L2 #W1 #T1 #T2 #_ #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
+  /3 width=3 by cpx_tau/
+| #G #L2 #W1 #W2 #T1 #_ #IHW12 #L1 #d #H elim (lleq_inv_flat … H) -H
+  /3 width=3 by cpx_ti/
+| #a #G #L1 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind … H) -H /4 width=3 by cpx_beta, leq_succ/
+| #a #G #L1 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind … H) -H /4 width=3 by cpx_theta, leq_succ/
 ]
 qed-.
+
+lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                      ∀L1. L1 ⋕[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
+/4 width=6 by lleq_cpx_trans_leq, lleq_fwd_length, leq_O_Y/ qed-. 
diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
index a70e151be..b54c386b9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
@@ -11,7 +11,7 @@ lemma lpx_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2,
 #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_dx … H2 ? I L1 V1) -H2 //
+  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
@@ -24,7 +24,7 @@ lemma lpx_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2,
   /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 … H2KL1 … HK1 HL1 … HTU1) -H2KL1
+  [ #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/