--- /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/notation/relations/exclaim_5.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* activate genv *)
+(* Basic_2A1: uses: snv *)
+inductive cnv (a) (h): relation3 genv lenv term ≝
+| cnv_sort: ∀G,L,s. cnv a h G L (⋆s)
+| cnv_zero: ∀I,G,K,V. cnv a h G K V → cnv a h G (K.ⓑ{I}V) (#0)
+| cnv_lref: ∀I,G,K,i. cnv a h G K (#i) → cnv a h G (K.ⓘ{I}) (#↑i)
+| cnv_bind: ∀p,I,G,L,V,T. cnv a h G L V → cnv a h G (L.ⓑ{I}V) T → cnv a h G L (ⓑ{p,I}V.T)
+| cnv_appl: ∀n,p,G,L,V,W0,T,U0. (a = Ⓣ → n = 1) → cnv a h G L V → cnv a h G L T →
+ ⦃G, L⦄ ⊢ V ➡*[1, h] W0 → ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0 → cnv a h G L (ⓐV.T)
+| cnv_cast: ∀G,L,U,T,U0. cnv a h G L U → cnv a h G L T →
+ ⦃G, L⦄ ⊢ U ➡*[h] U0 → ⦃G, L⦄ ⊢ T ➡*[1, h] U0 → cnv a h G L (ⓝU.T)
+.
+
+interpretation "context-sensitive native validity (term)"
+ 'Exclaim a h G L T = (cnv a h G L T).
+
+(* Basic inversion lemmas ***************************************************)
+
+fact cnv_inv_zero_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → X = #0 →
+ ∃∃I,K,V. ⦃G, K⦄ ⊢ V ![a, h] & L = K.ⓑ{I}V.
+#a #h #G #L #X * -G -L -X
+[ #G #L #s #H destruct
+| #I #G #K #V #HV #_ /2 width=5 by ex2_3_intro/
+| #I #G #K #i #_ #H destruct
+| #p #I #G #L #V #T #_ #_ #H destruct
+| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #H destruct
+| #G #L #U #T #U0 #_ #_ #_ #_ #H destruct
+]
+qed-.
+
+lemma cnv_inv_zero (a) (h): ∀G,L. ⦃G, L⦄ ⊢ #0 ![a, h] →
+ ∃∃I,K,V. ⦃G, K⦄ ⊢ V ![a, h] & L = K.ⓑ{I}V.
+/2 width=3 by cnv_inv_zero_aux/ qed-.
+
+fact cnv_inv_lref_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀i. X = #(↑i) →
+ ∃∃I,K. ⦃G, K⦄ ⊢ #i ![a, h] & L = K.ⓘ{I}.
+#a #h #G #L #X * -G -L -X
+[ #G #L #s #j #H destruct
+| #I #G #K #V #_ #j #H destruct
+| #I #G #L #i #Hi #j #H destruct /2 width=4 by ex2_2_intro/
+| #p #I #G #L #V #T #_ #_ #j #H destruct
+| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #j #H destruct
+| #G #L #U #T #U0 #_ #_ #_ #_ #j #H destruct
+]
+qed-.
+
+lemma cnv_inv_lref (a) (h): ∀G,L,i. ⦃G, L⦄ ⊢ #↑i ![a, h] →
+ ∃∃I,K. ⦃G, K⦄ ⊢ #i ![a, h] & L = K.ⓘ{I}.
+/2 width=3 by cnv_inv_lref_aux/ qed-.
+
+fact cnv_inv_gref_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀l. X = §l → ⊥.
+#a #h #G #L #X * -G -L -X
+[ #G #L #s #l #H destruct
+| #I #G #K #V #_ #l #H destruct
+| #I #G #K #i #_ #l #H destruct
+| #p #I #G #L #V #T #_ #_ #l #H destruct
+| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #l #H destruct
+| #G #L #U #T #U0 #_ #_ #_ #_ #l #H destruct
+]
+qed-.
+
+(* Basic_2A1: uses: snv_inv_gref *)
+lemma cnv_inv_gref (a) (h): ∀G,L,l. ⦃G, L⦄ ⊢ §l ![a, h] → ⊥.
+/2 width=8 by cnv_inv_gref_aux/ qed-.
+
+fact cnv_inv_bind_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] →
+ ∀p,I,V,T. X = ⓑ{p,I}V.T →
+ ∧∧ ⦃G, L⦄ ⊢ V ![a, h]
+ & ⦃G, L.ⓑ{I}V⦄ ⊢ T ![a, h].
+#a #h #G #L #X * -G -L -X
+[ #G #L #s #q #Z #X1 #X2 #H destruct
+| #I #G #K #V #_ #q #Z #X1 #X2 #H destruct
+| #I #G #K #i #_ #q #Z #X1 #X2 #H destruct
+| #p #I #G #L #V #T #HV #HT #q #Z #X1 #X2 #H destruct /2 width=1 by conj/
+| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #q #Z #X1 #X2 #H destruct
+| #G #L #U #T #U0 #_ #_ #_ #_ #q #Z #X1 #X2 #H destruct
+]
+qed-.
+
+(* Basic_2A1: uses: snv_inv_bind *)
+lemma cnv_inv_bind (a) (h): ∀p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⓑ{p,I}V.T ![a, h] →
+ ∧∧ ⦃G, L⦄ ⊢ V ![a, h]
+ & ⦃G, L.ⓑ{I}V⦄ ⊢ T ![a, h].
+/2 width=4 by cnv_inv_bind_aux/ qed-.
+
+fact cnv_inv_appl_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀V,T. X = ⓐV.T →
+ ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
+ ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
+#a #h #G #L #X * -L -X
+[ #G #L #s #X1 #X2 #H destruct
+| #I #G #K #V #_ #X1 #X2 #H destruct
+| #I #G #K #i #_ #X1 #X2 #H destruct
+| #p #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
+| #n #p #G #L #V #W0 #T #U0 #Ha #HV #HT #HVW0 #HTU0 #X1 #X2 #H destruct /3 width=7 by ex5_4_intro/
+| #G #L #U #T #U0 #_ #_ #_ #_ #X1 #X2 #H destruct
+]
+qed-.
+
+(* Basic_2A1: uses: snv_inv_appl *)
+lemma cnv_inv_appl (a) (h): ∀G,L,V,T. ⦃G, L⦄ ⊢ ⓐV.T ![a, h] →
+ ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
+ ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
+/2 width=3 by cnv_inv_appl_aux/ qed-.
+
+fact cnv_inv_cast_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀U,T. X = ⓝU.T →
+ ∃∃U0. ⦃G, L⦄ ⊢ U ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
+ ⦃G, L⦄ ⊢ U ➡*[h] U0 & ⦃G, L⦄ ⊢ T ➡*[1, h] U0.
+#a #h #G #L #X * -G -L -X
+[ #G #L #s #X1 #X2 #H destruct
+| #I #G #K #V #_ #X1 #X2 #H destruct
+| #I #G #K #i #_ #X1 #X2 #H destruct
+| #p #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
+| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #X1 #X2 #H destruct
+| #G #L #U #T #U0 #HV #HT #HU0 #HTU0 #X1 #X2 #H destruct /2 width=3 by ex4_intro/
+]
+qed-.
+
+(* Basic_2A1: uses: snv_inv_appl *)
+lemma cnv_inv_cast (a) (h): ∀G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ![a, h] →
+ ∃∃U0. ⦃G, L⦄ ⊢ U ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
+ ⦃G, L⦄ ⊢ U ➡*[h] U0 & ⦃G, L⦄ ⊢ T ➡*[1, h] U0.
+/2 width=3 by cnv_inv_cast_aux/ qed-.
--- /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_aaa.ma".
+include "basic_2/dynamic/cnv.ma".
+
+(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Forward lemmas on atomic arity assignment for terms **********************)
+
+(* Basic_2A1: uses: snv_fwd_aaa *)
+lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
+#a #h #G #L #T #H elim H -G -L -T
+[ /2 width=2 by aaa_sort, ex_intro/
+| #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
+| #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
+| #p * #G #L #V #T #_ #_ * #B #HV * #A #HA
+ /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
+| #n #p #G #L #V #W #T0 #U0 #_ #_ #_ #HVW #HTU0 * #B #HV * #X #HT
+ lapply (cpms_aaa_conf … HV … HVW) -HVW #H1W
+ lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
+ elim (aaa_inv_abst … H) -H #B0 #A #H2W #HU #H destruct
+ lapply (aaa_mono … H2W … H1W) -W #H destruct
+ /3 width=4 by aaa_appl, ex_intro/
+| #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
+ lapply (cpms_aaa_conf … HU … HU0) -HU0 #HU0
+ lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
+ lapply (aaa_mono … H … HU0) -U0 #H destruct
+ /3 width=3 by aaa_cast, ex_intro/
+]
+qed-.
--- /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/cnv.ma".
+
+(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Advanced dproperties *****************************************************)
+
+(* Basic_2A1: uses: snv_lref *)
+lemma cnv_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 cnv_zero/
+| #i #IH #L #HV #H
+ elim (drops_inv_succ … H) -H #J0 #K0 #HK0 #H destruct
+ /3 width=1 by cnv_lref/
+]
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: uses: snv_inv_lref *)
+lemma cnv_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 (cnv_inv_zero … H) -H #I #K #V #HV #H destruct
+ /3 width=5 by drops_refl, ex2_3_intro/
+| #i #IH #X #H
+ elim (cnv_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 csv_lifts (a) (h): ∀G. d_liftable1 (cnv 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 (cnv_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 cnv_lref_drops, fqup_lref, drops_inv_gen/
+| #l #HG #HK #HT #H1 #b #f #L #_ #X #_ destruct
+ elim (cnv_inv_gref … H1)
+| #p #I #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
+ elim (cnv_inv_bind … H1) -H1 #HV #HT
+ elim (lifts_inv_bind1 … H2) -H2 #W #U #HVW #HTU #H destruct
+ /5 width=8 by cnv_bind, drops_skip, ext2_pair/
+| #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
+ elim (cnv_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 cnv_appl, cpms_lifts_bi, lifts_bind/
+| #V #T #HG #HK #HT #H1 #b #f #L #HLK #X #H2 destruct
+ elim (cnv_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 cnv_cast, cpms_lifts_bi/
+]
+qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_2A1: uses: snv_inv_lift *)
+lemma cnv_inv_lifts (a) (h): ∀G. d_deliftable1 (cnv 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 (cnv_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 cnv_lref_drops, fqup_lref, drops_inv_F/
+| #l #HG #HL #HU #H1 #b #f #K #_ #X #_ destruct
+ elim (cnv_inv_gref … H1)
+| #p #I #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
+ elim (cnv_inv_bind … H1) -H1 #HW #HU
+ elim (lifts_inv_bind2 … H2) -H2 #V #T #HVW #HTU #H destruct
+ /5 width=8 by cnv_bind, drops_skip, ext2_pair/
+| #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
+ elim (cnv_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 cnv_appl/
+| #W #U #HG #HL #HU #H1 #b #f #K #HLK #X #H2 destruct
+ elim (cnv_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 cnv_cast/
+]
+qed-.
--- /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/s_computation/fqus_fqup.ma".
+include "basic_2/dynamic/cnv_drops.ma".
+
+(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with supclosure ***********************************************)
+
+(* Basic_2A1: uses: snv_fqu_conf *)
+lemma cnv_fqu_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
+#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+[ #I1 #G1 #L1 #V1 #H
+ elim (cnv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
+| * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
+ [ elim (cnv_inv_bind … H) -H //
+ | elim (cnv_inv_appl … H) -H //
+ | elim (cnv_inv_cast … H) -H //
+ ]
+| #p #I1 #G1 #L1 #V1 #T1 #H
+ elim (cnv_inv_bind … H) -H //
+| #p #I1 #G1 #L1 #V1 #T1 #H destruct
+| * #G1 #L1 #V1 #T1 #H
+ [ elim (cnv_inv_appl … H) -H //
+ | elim (cnv_inv_cast … H) -H //
+ ]
+| #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
+ /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
+]
+qed-.
+
+(* Basic_2A1: uses: snv_fquq_conf *)
+lemma cnv_fquq_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
+#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
+/2 width=5 by cnv_fqu_conf/
+qed-.
+
+(* Basic_2A1: uses: snv_fqup_conf *)
+lemma cnv_fqup_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
+#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/3 width=5 by fqup_strap1, cnv_fqu_conf/
+qed-.
+
+(* Basic_2A1: uses: snv_fqus_conf *)
+lemma cnv_fqus_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
+#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
+/2 width=5 by cnv_fqup_conf/
+qed-.
--- /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/fsb_aaa.ma".
+include "basic_2/dynamic/cnv_aaa.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Forward lemmas with strongly rst-normalizing closures ********************)
+
+(* Basic_2A1: uses: snv_fwd_fsb *)
+lemma cnv_fwd_fsb (a) (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ≥[h, o] 𝐒⦃G, L, T⦄.
+#a #h #o #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
+qed-.
+++ /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/notation/relations/exclaim_5.ma".
-include "basic_2/rt_computation/cpms.ma".
-
-(* NATIVE VALIDITY FOR TERMS ************************************************)
-
-(* activate genv *)
-(* Basic_2A1: uses: snv *)
-inductive nv (a) (h): relation3 genv lenv term ≝
-| nv_sort: ∀G,L,s. nv a h G L (⋆s)
-| nv_zero: ∀I,G,K,V. nv a h G K V → nv a h G (K.ⓑ{I}V) (#0)
-| nv_lref: ∀I,G,K,i. nv a h G K (#i) → nv a h G (K.ⓘ{I}) (#↑i)
-| nv_bind: ∀p,I,G,L,V,T. nv a h G L V → nv a h G (L.ⓑ{I}V) T → nv a h G L (ⓑ{p,I}V.T)
-| nv_appl: ∀n,p,G,L,V,W0,T,U0. (a = Ⓣ → n = 1) → nv a h G L V → nv a h G L T →
- ⦃G, L⦄ ⊢ V ➡*[1, h] W0 → ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0 → nv a h G L (ⓐV.T)
-| nv_cast: ∀G,L,U,T,U0. nv a h G L U → nv a h G L T →
- ⦃G, L⦄ ⊢ U ➡*[h] U0 → ⦃G, L⦄ ⊢ T ➡*[1, h] U0 → nv a h G L (ⓝU.T)
-.
-
-interpretation "native validity (term)"
- 'Exclaim a h G L T = (nv a h G L T).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact nv_inv_zero_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → X = #0 →
- ∃∃I,K,V. ⦃G, K⦄ ⊢ V ![a, h] & L = K.ⓑ{I}V.
-#a #h #G #L #X * -G -L -X
-[ #G #L #s #H destruct
-| #I #G #K #V #HV #_ /2 width=5 by ex2_3_intro/
-| #I #G #K #i #_ #H destruct
-| #p #I #G #L #V #T #_ #_ #H destruct
-| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #H destruct
-]
-qed-.
-
-lemma nv_inv_zero (a) (h): ∀G,L. ⦃G, L⦄ ⊢ #0 ![a, h] →
- ∃∃I,K,V. ⦃G, K⦄ ⊢ V ![a, h] & L = K.ⓑ{I}V.
-/2 width=3 by nv_inv_zero_aux/ qed-.
-
-fact nv_inv_lref_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀i. X = #(↑i) →
- ∃∃I,K. ⦃G, K⦄ ⊢ #i ![a, h] & L = K.ⓘ{I}.
-#a #h #G #L #X * -G -L -X
-[ #G #L #s #j #H destruct
-| #I #G #K #V #_ #j #H destruct
-| #I #G #L #i #Hi #j #H destruct /2 width=4 by ex2_2_intro/
-| #p #I #G #L #V #T #_ #_ #j #H destruct
-| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #j #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #j #H destruct
-]
-qed-.
-
-lemma nv_inv_lref (a) (h): ∀G,L,i. ⦃G, L⦄ ⊢ #↑i ![a, h] →
- ∃∃I,K. ⦃G, K⦄ ⊢ #i ![a, h] & L = K.ⓘ{I}.
-/2 width=3 by nv_inv_lref_aux/ qed-.
-
-fact nv_inv_gref_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀l. X = §l → ⊥.
-#a #h #G #L #X * -G -L -X
-[ #G #L #s #l #H destruct
-| #I #G #K #V #_ #l #H destruct
-| #I #G #K #i #_ #l #H destruct
-| #p #I #G #L #V #T #_ #_ #l #H destruct
-| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #l #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #l #H destruct
-]
-qed-.
-
-(* Basic_2A1: uses: snv_inv_gref *)
-lemma nv_inv_gref (a) (h): ∀G,L,l. ⦃G, L⦄ ⊢ §l ![a, h] → ⊥.
-/2 width=8 by nv_inv_gref_aux/ qed-.
-
-fact nv_inv_bind_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] →
- ∀p,I,V,T. X = ⓑ{p,I}V.T →
- ∧∧ ⦃G, L⦄ ⊢ V ![a, h]
- & ⦃G, L.ⓑ{I}V⦄ ⊢ T ![a, h].
-#a #h #G #L #X * -G -L -X
-[ #G #L #s #q #Z #X1 #X2 #H destruct
-| #I #G #K #V #_ #q #Z #X1 #X2 #H destruct
-| #I #G #K #i #_ #q #Z #X1 #X2 #H destruct
-| #p #I #G #L #V #T #HV #HT #q #Z #X1 #X2 #H destruct /2 width=1 by conj/
-| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #q #Z #X1 #X2 #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #q #Z #X1 #X2 #H destruct
-]
-qed-.
-
-(* Basic_2A1: uses: snv_inv_bind *)
-lemma nv_inv_bind (a) (h): ∀p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⓑ{p,I}V.T ![a, h] →
- ∧∧ ⦃G, L⦄ ⊢ V ![a, h]
- & ⦃G, L.ⓑ{I}V⦄ ⊢ T ![a, h].
-/2 width=4 by nv_inv_bind_aux/ qed-.
-
-fact nv_inv_appl_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀V,T. X = ⓐV.T →
- ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
- ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
-#a #h #G #L #X * -L -X
-[ #G #L #s #X1 #X2 #H destruct
-| #I #G #K #V #_ #X1 #X2 #H destruct
-| #I #G #K #i #_ #X1 #X2 #H destruct
-| #p #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #n #p #G #L #V #W0 #T #U0 #Ha #HV #HT #HVW0 #HTU0 #X1 #X2 #H destruct /3 width=7 by ex5_4_intro/
-| #G #L #U #T #U0 #_ #_ #_ #_ #X1 #X2 #H destruct
-]
-qed-.
-
-(* Basic_2A1: uses: snv_inv_appl *)
-lemma nv_inv_appl (a) (h): ∀G,L,V,T. ⦃G, L⦄ ⊢ ⓐV.T ![a, h] →
- ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
- ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
-/2 width=3 by nv_inv_appl_aux/ qed-.
-
-fact nv_inv_cast_aux (a) (h): ∀G,L,X. ⦃G, L⦄ ⊢ X ![a, h] → ∀U,T. X = ⓝU.T →
- ∃∃U0. ⦃G, L⦄ ⊢ U ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
- ⦃G, L⦄ ⊢ U ➡*[h] U0 & ⦃G, L⦄ ⊢ T ➡*[1, h] U0.
-#a #h #G #L #X * -G -L -X
-[ #G #L #s #X1 #X2 #H destruct
-| #I #G #K #V #_ #X1 #X2 #H destruct
-| #I #G #K #i #_ #X1 #X2 #H destruct
-| #p #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #n #p #G #L #V #W0 #T #U0 #_ #_ #_ #_ #_ #X1 #X2 #H destruct
-| #G #L #U #T #U0 #HV #HT #HU0 #HTU0 #X1 #X2 #H destruct /2 width=3 by ex4_intro/
-]
-qed-.
-
-(* Basic_2A1: uses: snv_inv_appl *)
-lemma nv_inv_cast (a) (h): ∀G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ![a, h] →
- ∃∃U0. ⦃G, L⦄ ⊢ U ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
- ⦃G, L⦄ ⊢ U ➡*[h] U0 & ⦃G, L⦄ ⊢ T ➡*[1, h] U0.
-/2 width=3 by nv_inv_cast_aux/ qed-.
+++ /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_aaa.ma".
-include "basic_2/dynamic/nv.ma".
-
-(* NATIVE VALIDITY FOR TERMS ************************************************)
-
-(* Forward lemmas on atomic arity assignment for terms **********************)
-
-(* Basic_2A1: uses: snv_fwd_aaa *)
-lemma nv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
-#a #h #G #L #T #H elim H -G -L -T
-[ /2 width=2 by aaa_sort, ex_intro/
-| #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
-| #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
-| #p * #G #L #V #T #_ #_ * #B #HV * #A #HA
- /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
-| #n #p #G #L #V #W #T0 #U0 #_ #_ #_ #HVW #HTU0 * #B #HV * #X #HT
- lapply (cpms_aaa_conf … HV … HVW) -HVW #H1W
- lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
- elim (aaa_inv_abst … H) -H #B0 #A #H2W #HU #H destruct
- lapply (aaa_mono … H2W … H1W) -W #H destruct
- /3 width=4 by aaa_appl, ex_intro/
-| #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
- lapply (cpms_aaa_conf … HU … HU0) -HU0 #HU0
- lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
- lapply (aaa_mono … H … HU0) -U0 #H destruct
- /3 width=3 by aaa_cast, ex_intro/
-]
-qed-.
+++ /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-.
+++ /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/s_computation/fqus_fqup.ma".
-include "basic_2/dynamic/nv_drops.ma".
-
-(* NATIVE VALIDITY FOR TERMS ************************************************)
-
-(* Properties with supclosure ***********************************************)
-
-(* Basic_2A1: uses: snv_fqu_conf *)
-lemma nv_fqu_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
-#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-[ #I1 #G1 #L1 #V1 #H
- elim (nv_inv_zero … H) -H #I2 #L2 #V2 #HV2 #H destruct //
-| * [ #p #I1 | * ] #G1 #L1 #V1 #T1 #H
- [ elim (nv_inv_bind … H) -H //
- | elim (nv_inv_appl … H) -H //
- | elim (nv_inv_cast … H) -H //
- ]
-| #p #I1 #G1 #L1 #V1 #T1 #H
- elim (nv_inv_bind … H) -H //
-| #p #I1 #G1 #L1 #V1 #T1 #H destruct
-| * #G1 #L1 #V1 #T1 #H
- [ elim (nv_inv_appl … H) -H //
- | elim (nv_inv_cast … H) -H //
- ]
-| #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
- /4 width=7 by nv_inv_lifts, drops_refl, drops_drop/
-]
-qed-.
-
-(* Basic_2A1: uses: snv_fquq_conf *)
-lemma nv_fquq_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
-#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [|*]
-/2 width=5 by nv_fqu_conf/
-qed-.
-
-(* Basic_2A1: uses: snv_fqup_conf *)
-lemma nv_fqup_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
-#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
-/3 width=5 by fqup_strap1, nv_fqu_conf/
-qed-.
-
-(* Basic_2A1: uses: snv_fqus_conf *)
-lemma nv_fqus_conf (a) (h): ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ T1 ![a, h] → ⦃G2, L2⦄ ⊢ T2 ![a, h].
-#a #h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H [|*]
-/2 width=5 by nv_fqup_conf/
-qed-.
+++ /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/fsb_aaa.ma".
-include "basic_2/dynamic/nv_aaa.ma".
-
-(* NATIVE VALIDITY FOR TERMS ************************************************)
-
-(* Forward lemmas with strongly rst-normalizing closures ********************)
-
-(* Basic_2A1: uses: snv_fwd_fsb *)
-lemma nv_fwd_fsb (a) (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ≥[h, o] 𝐒⦃G, L, T⦄.
-#a #h #o #G #L #T #H elim (nv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
-qed-.
-nv.ma nv_drops.ma nv_fqus.ma nv_aaa.ma nv_fsb.ma
+cnv.ma cnv_drops.ma cnv_fqus.ma cnv_aaa.ma cnv_fsb.ma
}
]
*)
- [ { "native validity" * } {
+ [ { "context-sensitive native validity" * } {
(*
[ [ "" ] "shnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] )" * ]
*)
- [ [ "for terms" ] "nv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" "nv_drops" + "nv_fqus" + "nv_aaa" + "nv_fsb" (* + "snv_lpr" + "snv_scpes" + "snv_preserve" *) * ]
+ [ [ "for terms" ] "cnv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" "cnv_drops" + "cnv_fqus" + "cnv_aaa" + "cnv_fsb" (* + "snv_lpr" + "snv_scpes" + "snv_preserve" *) * ]
}
]
}
projects / helm.git / commitdiff