X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fcnx%2Fcnx.etc;h=aaee69bfe88612a127ffa50967e603f69bffa5ed;hb=2002da6bcdbf12203a87a7d9630d738f67ede68c;hp=0259a08aa3442b5110878233fee9d2e28fe5ad12;hpb=a5a7eb39b9bad97d52d836ad1401329cff5b58a3;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/cnx/cnx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/cnx/cnx.etc
index 0259a08aa..aaee69bfe 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/cnx/cnx.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/cnx/cnx.etc
@@ -12,53 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/prednormal_5.ma".
 include "basic_2/reduction/cnr.ma".
-include "basic_2/reduction/cpx.ma".
-
-(* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
-
-definition cnx: ∀h. sd h → relation3 genv lenv term ≝
-                λh,o,G,L. NF … (cpx h o G L) (eq …).
-
-interpretation
-   "normality for context-sensitive extended reduction (term)"
-   'PRedNormal h o L T = (cnx h o L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cnx_inv_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃⋆s⦄ → deg h o s 0.
-#h #o #G #L #s #H elim (deg_total h o s)
-#d @(nat_ind_plus … d) -d // #d #_ #Hkd
-lapply (H (⋆(next h s)) ?) -H /2 width=2 by cpx_st/ -L -d #H
-lapply (destruct_tatom_tatom_aux … H) -H #H (**) (* destruct lemma needed *)
-lapply (destruct_sort_sort_aux … H) -H #H (**) (* destruct lemma needed *)
-lapply (next_lt h s) >H -H #H elim (lt_refl_false … H)
-qed-.
-
-lemma cnx_inv_delta: ∀h,o,I,G,L,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃#i⦄ → ⊥.
-#h #o #I #G #L #K #V #i #HLK #H
-elim (lift_total V 0 (i+1)) #W #HVW
-lapply (H W ?) -H [ /3 width=7 by cpx_delta/ ] -HLK #H destruct
-elim (lift_inv_lref2_be … HVW) -HVW /2 width=1 by ylt_inj/
-qed-.
-
-lemma cnx_inv_abst: ∀h,o,a,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃ⓛ{a}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃V⦄ ∧ ⦃G, L.ⓛV⦄ ⊢ ➡[h, o] 𝐍⦃T⦄.
-#h #o #a #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (ⓛ{a}V2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (ⓛ{a}V1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2 #H destruct //
-]
-qed-.
-
-lemma cnx_inv_abbr: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃-ⓓV.T⦄ →
-                    ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃V⦄ ∧ ⦃G, L.ⓓV⦄ ⊢ ➡[h, o] 𝐍⦃T⦄.
-#h #o #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2 #H destruct //
-]
-qed-.
-
 lemma cnx_inv_zeta: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃+ⓓV.T⦄ → ⊥.
 #h #o #G #L #V #T #H elim (is_lift_dec T 0 1)
 [ * #U #HTU
@@ -71,24 +28,6 @@ lemma cnx_inv_zeta: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃+ⓓV.T⦄ 
 ]
 qed-.
 
-lemma cnx_inv_appl: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃ⓐV.T⦄ →
-                    ∧∧ ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃V⦄ & ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ & 𝐒⦃T⦄.
-#h #o #G #L #V1 #T1 #HVT1 @and3_intro
-[ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpx_pair_sn/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpx_flat/ -HT2 #H destruct //
-| generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
-  [ elim (lift_total V1 0 1) #V2 #HV12
-    lapply (H (ⓓ{a}W1.ⓐV2.U1) ?) -H /3 width=3 by cpr_cpx, cpr_theta/ -HV12 #H destruct
-  | lapply (H (ⓓ{a}ⓝW1.V1.U1) ?) -H /3 width=1 by cpr_cpx, cpr_beta/ #H destruct
-  ]
-]
-qed-.
-
-lemma cnx_inv_eps: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃ⓝV.T⦄ → ⊥.
-#h #o #G #L #V #T #H lapply (H T ?) -H
-/2 width=4 by cpx_eps, discr_tpair_xy_y/
-qed-.
-
 (* Basic forward lemmas *****************************************************)
 
 lemma cnx_fwd_cnr: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
@@ -98,39 +37,9 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cnx_sort: ∀h,o,G,L,s. deg h o s 0 → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃⋆s⦄.
-#h #o #G #L #s #Hk #X #H elim (cpx_inv_sort1 … H) -H // * #d #Hkd #_
-lapply (deg_mono … Hkd Hk) -h -L <plus_n_Sm #H destruct
-qed.
-
-lemma cnx_sort_iter: ∀h,o,G,L,s,d. deg h o s d → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃⋆((next h)^d s)⦄.
-#h #o #G #L #s #d #Hkd
-lapply (deg_iter … d Hkd) -Hkd <minus_n_n /2 width=6 by cnx_sort/
-qed.
-
 lemma cnx_lref_free: ∀h,o,G,L,i. |L| ≤ i → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃#i⦄.
-#h #o #G #L #i #Hi #X #H elim (cpx_inv_lref1 … H) -H // *
-#I #K #V1 #V2 #HLK lapply (drop_fwd_length_lt2 … HLK) -HLK
-#H elim (lt_refl_false i) /2 width=3 by lt_to_le_to_lt/
-qed.
-
-lemma cnx_lref_atom: ∀h,o,G,L,i. ⬇[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃#i⦄.
 #h #o #G #L #i #HL @cnx_lref_free >(drop_fwd_length … HL) -HL //
 qed.
 
-lemma cnx_abst: ∀h,o,a,G,L,W,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃W⦄ → ⦃G, L.ⓛW⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ →
-                ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃ⓛ{a}W.T⦄.
-#h #o #a #G #L #W #T #HW #HT #X #H
-elim (cpx_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
->(HW … HW0) -W0 >(HT … HT0) -T0 //
-qed.
-
-lemma cnx_appl_simple: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃V⦄ → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ → 𝐒⦃T⦄ →
-                       ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃ⓐV.T⦄.
-#h #o #G #L #V #T #HV #HT #HS #X #H
-elim (cpx_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
->(HV … HV0) -V0 >(HT … HT0) -T0 //
-qed.
-
 axiom cnx_dec: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T1⦄ ∨
                ∃∃T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 & (T1 = T2 → ⊥).