matita/matita/contribs/lambda_delta/Basic_2/unfold/ldrops.ma

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  14
  15 include "Basic_2/substitution/ldrop.ma".
  16 include "Basic_2/unfold/lifts.ma".
  17
  18 (* GENERIC LOCAL ENVIRONMENT SLICING ****************************************)
  19
  20 inductive ldrops: list2 nat nat → relation lenv ≝
  21 | ldrops_nil : ∀L. ldrops ⟠ L L
  22 | ldrops_cons: ∀L1,L,L2,des,d,e.
  23                ldrops des L1 L → ⇩[d,e] L ≡ L2 → ldrops ({d, e} :: des) L1 L2
  24 .
  25
  26 interpretation "generic local environment slicing"
  27    'RDropStar des T1 T2 = (ldrops des T1 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma ldrops_skip: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → ∀V1,V2. ⇧*[des] V2 ≡ V1 →
  32                    ∀I. ⇩*[des + 1] L1. 𝕓{I} V1 ≡ L2. 𝕓{I} V2.
  33 #L1 #L2 #des #H elim H -L1 -L2 -des
  34 [ #L #V1 #V2 #HV12 #I
  35   >(lifts_inv_nil … HV12) -HV12 //
  36 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #V1 #V2 #H #I
  37   elim (lifts_inv_cons … H) -H /3 width=5/
  38 ].
  39 qed.
  40
  41 (* Basic_1: removed theorems 1: drop1_getl_trans
  42 *)
  43 (*
  44 lemma ldrops_inv_skip2: ∀des2,L1,I,K2,V2. ⇩*[des2] L1 ≡ K2. 𝕓{I} V2 →
  45                         ∀des,i. des ▭ i ≡ des2 →
  46                         ∃∃K1,V1,des1. des ▭ (i + 1) ≡ des1 &
  47                                       ⇩*[des1] K1 ≡ K2 &
  48                                       ⇧*[des1] V2 ≡ V1 &
  49                                       L1 = K1. 𝕓{I} V1.
  50 *)