+++ /dev/null
-
--include "basic_2/dynamic/cnv_cpce.ma".
--
- lemma pippo (h) (a) (G) (L0):
- ∀T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
- ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
- ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
- ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
- #h #a #G #L0 * *
- [ #s #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
-definition dropable_bi: predicate … ≝
- λR. ∀L1,L2. L1 ⪤[R] L2 → ∀b,f. 𝐔⦃f⦄ →
- ∀K1. ⇩*[b,f] L1 ≘ K1 → ∀K2. ⇩*[b,f] L2 ≘ K2 → K1 ⪤[R] K2.
-
-definition IH (h) (a): relation3 genv lenv term ≝
- λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
- ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
- ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
- ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
-
-lemma pippo_aux (h) (a) (G0) (L0) (T0):
- (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH h a G L T) →
- IH h a G0 L0 T0.
-#h #a #G0 #L0 * *
-[ #s #_ #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
-- elim (cpm_inv_sort1 … HX1) -HX1 #H #Hn destruct
-- lapply (cpce_inv_sort_sn … HX2) -HX2 #H destruct
-- /3 width=3 by cpce_sort, cpm_sort, ex2_intro/
- | #i #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
- elim (drops_F_uni L0 i)
- [
- | *
-| #i #IH #Hi #n #X1 #HX1 #X2 #HX2 #L1 #HL01
- elim (cnv_inv_lref_drops … Hi) -Hi #I #K0 #W0 #HLK0 #HW0
- elim (lpr_drops_conf … HLK0 … HL01) [| // ] #Y1 #H1 #HLK1
- elim (lex_inv_pair_sn … H1) -H1 #K1 #W1 #HK01 #HW01 #H destruct
- elim (cpce_inv_lref_sn_drops … HX2 … HLK0) -HX2 *
- [ #HI #H destruct
- elim (cpm_inv_lref1_drops … HX1) -HX1 *
- [ #H1 #H2 destruct -HW0 -HLK0 -IH
- @(ex2_intro … (#i)) [| // ]
- @cpce_zero_drops #n #p #Y1 #X1 #V1 #U1 #HLY1 #HWU1
- lapply (drops_mono … HLY1 … HLK1) -L1 #H2 destruct
- /4 width=12 by lpr_cpms_trans, cpms_step_sn/
- | #Y0 #W0 #W1 #HLY0 #HW01 #HWX1 -HI -HW0 -IH
- lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
- @(ex2_intro … X1) [| /2 width=6 by cpm_delta_drops/ ]
-
--
--(*
--lemma cpce_inv_eta_drops (h) (n) (G) (L) (i):
-- ∀X. ⦃G,L⦄ ⊢ #i ⬌η[h] X →
-- ∀K,W. ⇩*[i] L ≘ K.ⓛW →
-- ∀p,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
-- ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
-- ∀W2. ⇧*[↑i] V2 ≘ W2 → X = +ⓛW2.ⓐ#0.#↑i.
--
--theorem cpce_mono_cnv (h) (a) (G) (L):
-- ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
-- ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → T1 = T2.
--#h #a #G #L #T #HT
--*)
--- /dev/null
--- /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/dynamic/cnv_cpce.ma".
++
++(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
++
++definition IH (h) (a): relation3 genv lenv term ≝
++ λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
++ ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
++ ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
++ ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
++
++lemma pippo_aux (h) (a) (G0) (L0) (T0):
++ (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH h a G L T) →
++ IH h a G0 L0 T0.
++#h #a #G0 #L0 * *
++[ #s #_ #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
++ elim (cpm_inv_sort1 … HX1) -HX1 #H #Hn destruct
++ lapply (cpce_inv_sort_sn … HX2) -HX2 #H destruct
++ /3 width=3 by cpce_sort, cpm_sort, ex2_intro/
++| #i #IH #Hi #n #X1 #HX1 #X2 #HX2 #L1 #HL01
++ elim (cnv_inv_lref_drops … Hi) -Hi #I #K0 #W0 #HLK0 #HW0
++ elim (lpr_drops_conf … HLK0 … HL01) [| // ] #Y1 #H1 #HLK1
++ elim (lex_inv_pair_sn … H1) -H1 #K1 #W1 #HK01 #HW01 #H destruct
++ elim (cpce_inv_lref_sn_drops_bind … HX2 … HLK0) -HX2 *
++ [ #HI #H destruct
++ elim (cpm_inv_lref1_drops … HX1) -HX1 *
++ [ #H1 #H2 destruct -HW0 -HLK0 -IH
++ @(ex2_intro … (#i)) [| // ]
++ @cpce_zero_drops #n #p #Y1 #X1 #V1 #U1 #HLY1 #HWU1
++ lapply (drops_mono … HLY1 … HLK1) -L1 #H2 destruct
++ /4 width=12 by lpr_cpms_trans, cpms_step_sn/
++ | #Y0 #W0 #W1 #HLY0 #HW01 #HWX1 -HI -HW0 -IH
++ lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
++ @(ex2_intro … X1) [| /2 width=6 by cpm_delta_drops/ ]
++
++(*
++lemma cpce_inv_eta_drops (h) (n) (G) (L) (i):
++ ∀X. ⦃G,L⦄ ⊢ #i ⬌η[h] X →
++ ∀K,W. ⇩*[i] L ≘ K.ⓛW →
++ ∀p,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
++ ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
++ ∀W2. ⇧*[↑i] V2 ≘ W2 → X = +ⓛW2.ⓐ#0.#↑i.
++
++theorem cpce_mono_cnv (h) (a) (G) (L):
++ ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
++ ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → T1 = T2.
++#h #a #G #L #T #HT
++*)