matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrops.ma

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  15 include "basic_2/computation/lsubc_ldrop.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
  18
  19 (* Properties concerning generic local environment slicing ******************)
  20
  21 (* Basic_1: was: csubc_drop1_conf_rev *)
  22 lemma ldrops_lsubc_trans: ∀RR,RS,RP.
  23                           acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
  24                           ∀G,L1,K1,des. ⇩*[Ⓕ, des] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
  25                           ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⇩*[Ⓕ, des] L2 ≡ K2.
  26 #RR #RS #RP #Hacp #Hacr #G #L1 #K1 #des #H elim H -L1 -K1 -des
  27 [ /2 width=3 by ldrops_nil, ex2_intro/
  28 | #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
  29   elim (ldrop_lsubc_trans … Hacp Hacr … HLK1 … HK12) -Hacp -Hacr -K1 #K #HLK #HK2
  30   elim (IHL … HLK) -IHL -HLK /3 width=5 by ldrops_cons, ex2_intro/
  31 ]
  32 qed-.