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15 include "basic_2/computation/lsubc_drop.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
19 (* Properties concerning generic local environment slicing ******************)
21 (* Basic_1: was: csubc_drop1_conf_rev *)
22 lemma drops_lsubc_trans: ∀RR,RS,RP.
23 gcp RR RS RP → gcr RR RS RP RP →
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 #Hgcp #Hgcr #G #L1 #K1 #des #H elim H -L1 -K1 -des
27 [ /2 width=3 by drops_nil, ex2_intro/
28 | #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
29 elim (drop_lsubc_trans … Hgcp Hgcr … HLK1 … HK12) -Hgcp -Hgcr -K1 #K #HLK #HK2
30 elim (IHL … HLK) -IHL -HLK /3 width=5 by drops_cons, ex2_intro/