matita/matita/contribs/lambda_delta/basic_2/unfold/thin_delift.ma

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  14
  15 include "basic_2/unfold/tpss_alt.ma".
  16 include "basic_2/unfold/ltpss_ltpss.ma".
  17 include "basic_2/unfold/delift_alt.ma".
  18 include "basic_2/unfold/thin.ma".
  19
  20 (* DELIFT ON LOCAL ENVIRONMENTS *********************************************)
  21
  22 (* Properties on deflift on terms *******************************************)
  23
  24 lemma thin_delift1: ∀L1,L2,d,e. L1 [d, e] ≡ L2 → ∀V1,V2. L1 ⊢ V1 [d, e] ≡ V2 →
  25                     ∀I. L1.ⓑ{I}V1 [d + 1, e] ≡ L2.ⓑ{I}V2.
  26 #L1 #L2 #d #e * #L #HL1 #HL2 #V1 #V2 * #V #HV1 #HV2 #I
  27 elim (ltpss_tpss_conf … HV1 … HL1) -HV1 #V0 #HV10 #HV0
  28 elim (tpss_inv_lift1_be … HV0 … HL2 … HV2 ? ?) -HV0 // <minus_n_n #X #H1 #H2
  29 lapply (tpss_inv_refl_O2 … H1) -H1 #H destruct
  30 lapply (lift_mono … H2 … HV2) -H2 #H destruct /3 width=5/
  31 qed.
  32
  33 axiom delift_tpss_conf_be: ∀L,U1,U2,d,e. L ⊢ U1 [d, e] ▶* U2 →
  34                            ∀T1,dd,ee. L ⊢ U1 [dd, ee] ≡ T1 → ∀K. L [dd, ee] ≡ K →
  35                            d ≤ dd → dd + ee ≤ d + e →
  36                            ∃∃T2. K ⊢ T1 [dd - d, e - ee] ▶* T2 & L ⊢ U2 [dd, ee] ≡ T2.
  37 (*
  38 #L #U1 #U2 #d #e #H @(tpss_ind_alt … H) -L -U1 -U2 -d -e
  39 [ #L * #i #d #e #X #dd #ee #H
  40   [ >(delift_inv_sort1 … H) -X /2 width=3/
  41   | elim (delift_inv_lref1 … H) -H * [1,3: /3 width=3/ | /3 width=6/ ]
  42   | >(delift_inv_gref1 … H) -X /2 width=3/
  43   ]
  44 | #L #K1 #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK1 #_ #HVW2 #IHV12 #T1 #dd #ee #H #K2 #HLK2 #Hdd #Hddee
  45   lapply
  46
  47     @(ex2_1_intro … X) // /2 width=6/
  48 *)