- advances on drops

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_new / drops / drops.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops.etc
index 86ca4c76a43d973aa3ee394c156ed61f4a2f7a26..5d51b83c850108ebc030f3156e81d2af1824aca6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops.etc
@@ -1,53 +1,2 @@
-lemma drop_split: ∀L1,L2,l,m2,s. ⬇[s, l, m2] L1 ≡ L2 → ∀m1. m1 ≤ m2 →
-                  ∃∃L. ⬇[s, l, m2 - m1] L1 ≡ L & ⬇[s, l, m1] L ≡ L2.
-#L1 #L2 #l #m2 #s #H elim H -L1 -L2 -l -m2
-[ #l #m2 #Hs #m1 #Hm12 @(ex2_intro … (⋆))
-  @drop_atom #H lapply (Hs H) -s #H destruct /2 width=1 by le_n_O_to_eq/
-| #I #L1 #V #m1 #Hm1 lapply (le_n_O_to_eq … Hm1) -Hm1
-  #H destruct /2 width=3 by ex2_intro/
-| #I #L1 #L2 #V #m2 #HL12 #IHL12 #m1 @(nat_ind_plus … m1) -m1
-  [ /3 width=3 by drop_drop, ex2_intro/
-  | -HL12 #m1 #_ #Hm12 lapply (le_plus_to_le_r … Hm12) -Hm12
-    #Hm12 elim (IHL12 … Hm12) -IHL12 >minus_plus_plus_l
-    #L #HL1 #HL2 elim (lt_or_ge (|L1|) (m2-m1)) #H0
-    [ elim (drop_inv_O1_gt … HL1 H0) -HL1 #H1 #H2 destruct
-      elim (drop_inv_atom1 … HL2) -HL2 #H #_ destruct
-      @(ex2_intro … (⋆)) [ @drop_O1_ge normalize // ]
-      @drop_atom #H destruct
-    | elim (drop_O1_pair … HL1 H0 I V) -HL1 -H0 /3 width=5 by drop_drop, ex2_intro/
-    ]
-  ]
-| #I #L1 #L2 #V1 #V2 #l #m2 #_ #HV21 #IHL12 #m1 #Hm12 elim (IHL12 … Hm12) -IHL12
-  #L #HL1 #HL2 elim (lift_split … HV21 l m1) -HV21 /3 width=5 by drop_skip, ex2_intro/
-]
-qed-.
-
 lemma drop_inv_refl: ∀L,l,m. ⬇[Ⓕ, l, m] L ≡ L → m = 0.
 /2 width=5 by drop_inv_length_eq/ qed-.
-
-fact drop_inv_FT_aux: ∀L1,L2,s,l,m. ⬇[s, l, m] L1 ≡ L2 →
-                      ∀I,K,V. L2 = K.ⓑ{I}V → s = Ⓣ → l = 0 →
-                      ⬇[Ⓕ, l, m] L1 ≡ K.ⓑ{I}V.
-#L1 #L2 #s #l #m #H elim H -L1 -L2 -l -m
-[ #l #m #_ #J #K #W #H destruct
-| #I #L #V #J #K #W #H destruct //
-| #I #L1 #L2 #V #m #_ #IHL12 #J #K #W #H1 #H2 destruct
-  /3 width=1 by drop_drop/
-| #I #L1 #L2 #V1 #V2 #l #m #_ #_ #_ #J #K #W #_ #_ #H
-  elim (ysucc_inv_O_dx … H)
-]
-qed-.
-
-lemma drop_inv_FT: ∀I,L,K,V,m. ⬇[Ⓣ, 0, m] L ≡ K.ⓑ{I}V → ⬇[m] L ≡
-K.ⓑ{I}V.
-/2 width=5 by drop_inv_FT_aux/ qed.
-
-lemma drop_inv_gen: ∀I,L,K,V,s,m. ⬇[s, 0, m] L ≡ K.ⓑ{I}V → ⬇[m] L ≡
-K.ⓑ{I}V.
-#I #L #K #V * /2 width=1 by drop_inv_FT/
-qed-.
-
-lemma drop_inv_T: ∀I,L,K,V,s,m. ⬇[Ⓣ, 0, m] L ≡ K.ⓑ{I}V → ⬇[s, 0, m] L
-≡ K.ⓑ{I}V.
-#I #L #K #V * /2 width=1 by drop_inv_FT/
-qed-.