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

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  14
  15 include "ground/xoa/ex_4_5.ma".
  16 include "basic_2/rt_transition/cpg_drops.ma".
  17 include "basic_2/rt_transition/cpx.ma".
  18
  19 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 (* Basic_2A1: was: cpx_delta *)
  24 lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
  25                        ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⬈[h] V2 →
  26                        ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈[h] W2.
  27 #h * #G #L #K #V #V2 #W2 #i #HLK *
  28 /3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
  29 qed.
  30
  31 (* Advanced inversion lemmas ************************************************)
  32
  33 (* Basic_2A1: was: cpx_inv_atom1 *)
  34 lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ❪G,L❫ ⊢ ⓪[I] ⬈[h] T2 →
  35                            ∨∨ T2 = ⓪[I]
  36                             | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s
  37                             | ∃∃J,K,V,V2,i. ⇩[i] L ≘ K.ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
  38                                             ⇧[↑i] V2 ≘ T2 & I = LRef i.
  39 #h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
  40 /4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
  41 qed-.
  42
  43 (* Basic_2A1: was: cpx_inv_lref1 *)
  44 lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #i ⬈[h] T2 →
  45                            T2 = #i ∨
  46                            ∃∃J,K,V,V2. ⇩[i] L ≘ K. ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
  47                                        ⇧[↑i] V2 ≘ T2.
  48 #h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
  49 /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
  50 qed-.
  51
  52 (* Properties with generic slicing for local environments *******************)
  53
  54 (* Basic_2A1: includes: cpx_lift *)
  55 lemma cpx_lifts_sn: ∀h,G. d_liftable2_sn … lifts (cpx h G).
  56 #h #G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
  57 elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
  58 /3 width=4 by ex2_intro, ex_intro/
  59 qed-.
  60
  61 lemma cpx_lifts_bi: ∀h,G. d_liftable2_bi … lifts (cpx h G).
  62 #h #G #K #T1 #T2 * /3 width=10 by cpg_lifts_bi, ex_intro/
  63 qed-.
  64
  65 (* Inversion lemmas with generic slicing for local environments *************)
  66
  67 (* Basic_2A1: includes: cpx_inv_lift1 *)
  68 lemma cpx_inv_lifts_sn: ∀h,G. d_deliftable2_sn … lifts (cpx h G).
  69 #h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
  70 elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
  71 /3 width=4 by ex2_intro, ex_intro/
  72 qed-.
  73
  74 lemma cpx_inv_lifts_bi: ∀h,G. d_deliftable2_bi …lifts (cpx h G).
  75 #h #G #L #U1 #U2 * /3 width=10 by cpg_inv_lifts_bi, ex_intro/
  76 qed-.