new definition of llor gives a long awaited lemma :),

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / llor_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/llor_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/llor_alt.ma
deleted file mode 100644 (file)
index b62a002..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/llor_alt.ma
+++ /dev/null
@@ -1,66 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/relocation/lpx_sn_alt.ma".
-include "basic_2/substitution/llor.ma".
-
-(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
-
-(* Alternative definition ***************************************************)
-
-theorem llor_intro_alt: ∀T,L2,L1,L. |L1| ≤ |L2| → |L1| = |L| →
-                        (∀I1,I,K1,K,V1,V,i. ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L ≡ K.ⓑ{I}V →
-                           (K1 ⊢ |L2|-|L1|+i ~ϵ 𝐅*[yinj 0]⦃T⦄ → I1 = I ∧ V1 = V) ∧
-                           (∀I2,K2,V2. (K1 ⊢ |L2|-|L1|+i ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) →
-                                       ⇩[|L2|-|L1|+i] L2 ≡ K2.ⓑ{I2}V2 → I1 = I ∧ V2 = V
-                           )
-                        ) → L1 ⩖[T] L2 ≡ L.
-#T #L2 #L1 #L #HL12 #HL1 #IH @lpx_sn_intro_alt // -HL1
-#I1 #I #K1 #K #V1 #V #i #HLK1 #HLK
-lapply (ldrop_fwd_length_minus4 … HLK1)
-lapply (ldrop_fwd_length_le4 … HLK1)
-normalize in ⊢ (%→%→?); #HKL1 #Hi
-lapply (plus_minus_minus_be_aux … HL12 Hi) // -Hi <minus_plus #Hi
-lapply (transitive_le … HKL1 HL12) -HKL1 -HL12 #HKL1
-elim (IH … HLK1 HLK) -IH -HLK1 -HLK #IH1 #IH2
-elim (cofrees_dec K1 T 0 (|L2|-|L1|+i))
-[ -IH2 #HT elim (IH1 … HT) -IH1
-  #HI1 #HV1 @conj // <HV1 -V @clor_sn // <Hi -Hi //
-| -IH1 #HnT elim (ldrop_O1_lt (Ⓕ) L2 (|L2|-|L1|+i)) /2 width=1 by monotonic_lt_minus_l/
-  #I2 #K2 #V2 #HLK2 elim (IH2 … HLK2) -IH2 /2 width=1 by/
-  #HI1 #HV2 @conj // <HV2 -V @(clor_dx … I2 K2) // <Hi -Hi /2 width=1 by/
-]
-qed.
-
-theorem llor_inv_alt: ∀T,L2,L1,L. L1 ⩖[T] L2 ≡ L → |L1| ≤ |L2| →
-                      |L1| = |L| ∧
-                      (∀I1,I,K1,K,V1,V,i.
-                         ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L ≡ K.ⓑ{I}V →
-                         (∧∧ K1 ⊢ |L2|-|L1|+i ~ϵ 𝐅*[yinj 0]⦃T⦄ & I1 = I & V1 = V) ∨
-                         (∃∃I2,K2,V2. (K1 ⊢ |L2|-|L1|+i ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) &
-                                      ⇩[|L2|-|L1|+i] L2 ≡ K2.ⓑ{I2}V2 &
-                                      I1 = I & V2 = V
-                         )
-                      ).
-#T #L2 #L1 #L #H #HL12 elim (lpx_sn_inv_alt … H) -H
-#HL1 #IH @conj // -HL1
-#I1 #I #K1 #K #V1 #V #i #HLK1 #HLK
-lapply (ldrop_fwd_length_minus4 … HLK1)
-lapply (ldrop_fwd_length_le4 … HLK1)
-normalize in ⊢ (%→%→?); #HKL1 #Hi
-lapply (plus_minus_minus_be_aux … HL12 Hi) // -HL12 -Hi -HKL1
-<minus_plus #Hi >Hi -Hi
-elim (IH … HLK1 HLK) -IH #HI1 *
-/4 width=5 by or_introl, or_intror, and3_intro, ex4_3_intro/
-qed-.