matita/matita/contribs/lambdadelta/basic_2A/computation/lsubc_drops.ma

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  15 include "basic_2A/computation/lsubc_drop.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
  18
  19 (* Properties concerning generic local environment slicing ******************)
  20
  21 (* Basic_1: was: csubc_drop1_conf_rev *)
  22 lemma drops_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
  23                          ∀G,L1,K1,cs. ⬇*[Ⓕ, cs] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
  24                          ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[Ⓕ, cs] L2 ≡ K2.
  25 #RR #RS #RP #Hgcp #G #L1 #K1 #cs #H elim H -L1 -K1 -cs
  26 [ /2 width=3 by drops_nil, ex2_intro/
  27 | #L1 #L #K1 #cs #l #m #_ #HLK1 #IHL #K2 #HK12
  28   elim (drop_lsubc_trans … Hgcp … HLK1 … HK12) -Hgcp -K1 #K #HLK #HK2
  29   elim (IHL … HLK) -IHL -HLK /3 width=5 by drops_cons, ex2_intro/
  30 ]
  31 qed-.