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

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