+++ /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/substitution/cpye_lift.ma".
-include "basic_2/substitution/lleq_alt.ma".
-
-(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
-
-(* Forward lemmas on evaluation for extended substitution *******************)
-
-lemma lleq_fwd_cpye: ∀L1,L2,T,d. L1 ⋕[T, d] L2 → ∀G,T1. ⦃G, L1⦄ ⊢ T ▶*[d, ∞] 𝐍⦃T1⦄ →
- ∀T2. ⦃G, L2⦄ ⊢ T ▶*[d, ∞] 𝐍⦃T2⦄ → T1 = T2.
-#L1 #L2 #T #d #H @(lleq_ind_alt … H) -L1 -L2 -T -d
-[ #L1 #L2 #d #k #_ #G #T1 #H1 #T2 #H2
- >(cpye_inv_sort1 … H1) -H1 >(cpye_inv_sort1 … H2) -H2 //
-| #L1 #L2 #d #i #_ #Hid #G #T1 #H1 #T2 #H2
- >(cpye_inv_lref1_free … H1) -H1 [ >(cpye_inv_lref1_free … H2) -H2 ]
- /2 width=1 by or3_intro2/
-| #I1 #I2 #L1 #L2 #K1 #K2 #V #d #i #Hdi #HLK1 #HLK2 #_ #IHV #G #T1 #H1 #T2 #H2
- elim (cpye_inv_lref1_subst_ex … H1 … HLK1) -H1 -HLK1 //
- elim (cpye_inv_lref1_subst_ex … H2 … HLK2) -H2 -HLK2 //
- >yminus_Y_inj #V2 #HV2 #HVT2 #V1 #HV1 #HVT1
- lapply (IHV … HV1 … HV2) -IHV -HV1 -HV2 #H destruct /2 width=5 by lift_mono/
-| #L1 #L2 #d #i #_ #HL1 #HL2 #G #T1 #H1 #T2 #H2
- >(cpye_inv_lref1_free … H1) -H1 [ >(cpye_inv_lref1_free … H2) -H2 ]
- /2 width=1 by or3_intro0/
-| #L1 #L2 #d #p #_ #G #T1 #H1 #T2 #H2
- >(cpye_inv_gref1 … H1) -H1 >(cpye_inv_gref1 … H2) -H2 //
-| #a #I #L1 #L2 #V #T #d #_ #_ #IHV #IHT #G #X1 #H1 #X2 #H2
- elim (cpye_inv_bind1 … H1) -H1 #V1 #T1 #HV1 #HT1 #H destruct
- elim (cpye_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
- /3 width=3 by eq_f2/
-| #I #L1 #L2 #V #T #d #_ #_ #IHV #IHT #G #X1 #H1 #X2 #H2
- elim (cpye_inv_flat1 … H1) -H1 #V1 #T1 #HV1 #HT1 #H destruct
- elim (cpye_inv_flat1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
- /3 width=3 by eq_f2/
-]
-qed-.