+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/rt_computation/cpms_drops.ma".
-include "basic_2/dynamic/nv.ma".
-
-(* NATIVE VALIDITY FOR TERMS ************************************************)
-
-(* Advanced dproperties *****************************************************)
-
-(* Basic_2A1: uses: snv_lref *)
-lemma nv_lref_drops (a) (h) (G): ∀I,K,V,i,L. ⦃G, K⦄ ⊢ V ![a, h] →
- ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, L⦄ ⊢ #i ![a, h].
-#a #h #G #I #K #V #i elim i -i
-[ #L #HV #H
- lapply (drops_fwd_isid … H ?) -H // #H destruct
- /2 width=1 by nv_zero/
-| #i #IH #L #HV #H
- elim (drops_inv_succ … H) -H #J0 #K0 #HK0 #H destruct
- /3 width=1 by nv_lref/
-]
-qed.
-
-(* Advanced inversion lemmas ************************************************)
-
-(* Basic_2A1: uses: snv_inv_lref *)
-lemma nv_inv_lref_drops (a) (h) (G):
- ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
- ∃∃I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ![a, h].
-#a #h #G #i elim i -i
-[ #L #H
- elim (nv_inv_zero … H) -H #I #K #V #HV #H destruct
- /3 width=5 by drops_refl, ex2_3_intro/
-| #i #IH #X #H
- elim (nv_inv_lref … H) -H #I #L #HL #H destruct
- elim (IH … HL) -IH -HL #J #K #V #HLK #HV
- /3 width=5 by drops_drop, ex2_3_intro/
-]
-qed-.
-
-(* Properties with generic slicing for local environments *******************)
-
-(* Basic_2A1: uses: snv_lift *)
-lemma sv_lifts (a) (h): ∀G. d_liftable1 (nv a h G).
-#a #h #G #K #T
-@(fqup_wf_ind_eq (Ⓣ) … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * * [|||| * ]
-[ #s #HG #HK #HT #_ #b #f #L #_ #X #H2 destruct
- >(lifts_inv_sort1 … H2) -X -K -f //
-| #i #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
- elim (nv_inv_lref_drops … H1) -H1 #I0 #K0 #V #HK0 #HV
- elim (lifts_inv_lref1 … H2) -H2 #j #Hf #H destruct
-(**) (* this should be a lemma *)
- lapply (drops_trans … HLK … HK0 ??) -HLK [3,6: |*: // ] #H
- elim (drops_split_trans … H) -H [1,6: |*: /2 width=6 by after_uni_dx/ ] #Y #HL #HY
- lapply (drops_tls_at … Hf … HY) -HY #HY
- elim (drops_inv_skip2 … HY) -HY #Z #L0 #HLK0 #HZ #H destruct
- elim (liftsb_inv_pair_sn … HZ) -HZ #W #HVW #H destruct
-(**) (* end of the lemma *)
- /4 width=8 by nv_lref_drops, fqup_lref, drops_inv_gen/
-| #l #HG #HK #HT #H1 #b #f #L #_ #X #_ destruct
- elim (nv_inv_gref … H1)
-| #p #I #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
- elim (nv_inv_bind … H1) -H1 #HV #HT
- elim (lifts_inv_bind1 … H2) -H2 #W #U #HVW #HTU #H destruct
- /5 width=8 by nv_bind, drops_skip, ext2_pair/
-| #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
- elim (nv_inv_appl … H1) #n #p #W0 #U0 #Ha #HV #HT #HVW0 #HTW0
- elim (lifts_inv_flat1 … H2) -H2 #W #U #HVW #HTU #H destruct
- elim (lifts_total W0 f)
- elim (lifts_total U0 (⫯f))
- /4 width=17 by nv_appl, cpms_lifts_bi, lifts_bind/
-| #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
- elim (nv_inv_cast … H1) #U0 #HV #HT #HVU0 #HTU0
- elim (lifts_inv_flat1 … H2) -H2 #W #U #HVW #HTU #H destruct
- elim (lifts_total U0 f)
- /3 width=12 by nv_cast, cpms_lifts_bi/
-]
-qed-.
-
-(* Inversion lemmas with generic slicing for local environments *************)
-
-(* Basic_2A1: uses: snv_inv_lift *)
-lemma nv_inv_lifts (a) (h): ∀G. d_deliftable1 (nv a h G).
-#a #h #G #L #U
-@(fqup_wf_ind_eq (Ⓣ) … G L U) -G -L -U #G0 #L0 #U0 #IH #G #L * * [|||| * ]
-[ #s #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
- >(lifts_inv_sort2 … H2) -X -L -f //
-| #j #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
- elim (nv_inv_lref_drops … H1) -H1 #I0 #L0 #W #HL0 #HW
- elim (lifts_inv_lref2 … H2) -H2 #i #Hf #H destruct
-(**) (* this should be a lemma *)
- lapply (drops_split_div … HLK (𝐔❴i❵) ???) -HLK [4,8: * |*: // ] #Y0 #HK #HLY0
- lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0
- lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0
- elim (drops_inv_skip1 … HLY0) -HLY0 #Z #K0 #HLK0 #HZ #H destruct
- elim (liftsb_inv_pair_dx … HZ) -HZ #V #HVW #H destruct
-(**) (* end of the lemma *)
- /4 width=8 by nv_lref_drops, fqup_lref, drops_inv_F/
-| #l #HG #HL #HU #H1 #b #f #K #_ #X #_ destruct
- elim (nv_inv_gref … H1)
-| #p #I #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
- elim (nv_inv_bind … H1) -H1 #HW #HU
- elim (lifts_inv_bind2 … H2) -H2 #V #T #HVW #HTU #H destruct
- /5 width=8 by nv_bind, drops_skip, ext2_pair/
-| #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
- elim (nv_inv_appl … H1) #n #p #W0 #U0 #Ha #HW #HU #HW0 #HU0
- elim (lifts_inv_flat2 … H2) -H2 #V #T #HVW #HTU #H destruct
- elim (cpms_inv_lifts_sn … HW0 … HLK … HVW) -HW0 #V0 #HVW0 #HV0
- elim (cpms_inv_lifts_sn … HU0 … HLK … HTU) -HU0 #X0 #H #HT0
- elim (lifts_inv_bind2 … H) -H #X #T0 #HX #HTU0 #H destruct
- lapply (lifts_inj … HX … HVW0) -HX #H destruct
- /3 width=8 by nv_appl/
-| #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
- elim (nv_inv_cast … H1) #U0 #HW #HU #HWU0 #HU0
- elim (lifts_inv_flat2 … H2) -H2 #V #T #HVW #HTU #H destruct
- elim (cpms_inv_lifts_sn … HWU0 … HLK … HVW) -HWU0 #V0 #HVU0 #HV0
- elim (cpms_inv_lifts_sn … HU0 … HLK … HTU) -HU0 #X #HX #HTV0
- lapply (lifts_inj … HX … HVU0) -HX #H destruct
- /3 width=8 by nv_cast/
-]
-qed-.
projects / helm.git / blobdiff