matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx_drops.ma

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/cpx_drops.ma".
  16 include "basic_2/rt_transition/cnx.ma".
  17
  18 (* NORMAL TERMS FOR UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ******)
  19
  20 (* Properties with generic slicing ******************************************)
  21
  22 lemma cnx_lref_atom: ∀h,o,G,L,i. ⬇*[i] L ≡ ⋆ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃#i⦄.
  23 #h #o #G #L #i #Hi #X #H elim (cpx_inv_lref1_drops … H) -H // *
  24 #I #K #V1 #V2 #HLK lapply (drops_mono … Hi … HLK) -L #H destruct
  25 qed.
  26
  27 (* Inversion lemmas with generic slicing ************************************)
  28
  29 (* Basic_2A1: was: cnx_inv_delta *)
  30 lemma cnx_inv_lref_pair: ∀h,o,I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃#i⦄ → ⊥.
  31 #h #o #I #G #L #K #V #i #HLK #H
  32 elim (lifts_total V (𝐔❴⫯i❵)) #W #HVW
  33 lapply (H W ?) -H /2 width=7 by cpx_delta_drops/ -HLK
  34 #H lapply (tdeq_inv_lref1 … H) -H #H destruct
  35 /2 width=5 by lifts_inv_lref2_uni_lt/
  36 qed-.
  37
  38 (*
  39 (* Relocation properties ****************************************************)
  40
  41 lemma cnx_lift: ∀h,o,G,L0,L,T,T0,c,l,k. ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄ → ⬇[c, l, k] L0 ≡ L →
  42                 ⬆[l, k] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡[h, o] 𝐍⦃T0⦄.
  43 #h #o #G #L0 #L #T #T0 #c #l #k #HLT #HL0 #HT0 #X #H
  44 elim (cpx_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
  45 <(HLT … HT1) in HT0; -L #HT0
  46 >(lift_mono … HT10 … HT0) -T1 -X //
  47 qed.
  48
  49 lemma cnx_inv_lift: ∀h,o,G,L0,L,T,T0,c,l,k. ⦃G, L0⦄ ⊢ ➡[h, o] 𝐍⦃T0⦄ → ⬇[c, l, k] L0 ≡ L →
  50                     ⬆[l, k] T ≡ T0 → ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T⦄.
  51 #h #o #G #L0 #L #T #T0 #c #l #k #HLT0 #HL0 #HT0 #X #H
  52 elim (lift_total X l k) #X0 #HX0
  53 lapply (cpx_lift … H … HL0 … HT0 … HX0) -L #HTX0
  54 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
  55 >(lift_inj … H … HT0) -T0 -X -l -k //
  56 qed-.
  57 *)