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-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
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-(* v GNU General Public License Version 2 *)
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-
-include "basic_2/multiple/llpx_sn_alt.ma".
-include "basic_2/multiple/lleq.ma".
-
-(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
-
-(* Alternative definition (not recursive) ***********************************)
-
-theorem lleq_intro_alt: ∀L1,L2,T,l. |L1| = |L2| →
- (∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
- ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
- I1 = I2 ∧ V1 = V2
- ) → L1 ≡[T, l] L2.
-#L1 #L2 #T #l #HL12 #IH @llpx_sn_alt_inv_llpx_sn @conj // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
-@(IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 //
-qed.
-
-theorem lleq_inv_alt: ∀L1,L2,T,l. L1 ≡[T, l] L2 →
- |L1| = |L2| ∧
- ∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
- ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
- I1 = I2 ∧ V1 = V2.
-#L1 #L2 #T #l #H elim (llpx_sn_llpx_sn_alt … H) -H
-#HL12 #IH @conj //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
-@(IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 //
-qed-.