matita/matita/contribs/lambdadelta/basic_2/unfold/ldrops_ldrop.ma

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  14
  15 include "basic_2/substitution/ldrop_ldrop.ma".
  16 include "basic_2/unfold/ldrops.ma".
  17
  18 (* GENERIC LOCAL ENVIRONMENT SLICING ****************************************)
  19
  20 (* Properties concerning basic local environment slicing ********************)
  21
  22 lemma ldrops_ldrop_trans: ∀L1,L,des. ⇩*[des] L1 ≡ L → ∀L2,i. ⇩[0, i] L ≡ L2 →
  23                           ∃∃L0,des0,i0. ⇩[0, i0] L1 ≡ L0 & ⇩*[des0] L0 ≡ L2 &
  24                                         @⦃i, des⦄ ≡ i0 & des ▭ i ≡ des0.
  25 #L1 #L #des #H elim H -L1 -L -des
  26 [ /2 width=7/
  27 | #L1 #L3 #L #des3 #d #e #_ #HL3 #IHL13 #L2 #i #HL2
  28   elim (lt_or_ge i d) #Hid
  29   [ elim (ldrop_trans_le … HL3 … HL2 ?) -L /2 width=2/ #L #HL3 #HL2
  30     elim (IHL13 … HL3) -L3 /3 width=7/
  31   | lapply (ldrop_trans_ge … HL3 … HL2 ?) -L // #HL32
  32     elim (IHL13 … HL32) -L3 /3 width=7/
  33   ]
  34 ]
  35 qed-.