matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma

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  14
  15 include "basic_2/relocation/drops_ceq.ma".
  16 include "basic_2/relocation/drops_lexs.ma".
  17
  18 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
  19
  20 (* Properties with ranged equivalence for local environments ****************)
  21
  22 lemma lreq_dedropable: dedropable_sn lreq.
  23 @lexs_liftable_dedropable
  24 /2 width=6 by cfull_lift, ceq_lift, cfull_refl, ceq_refl/
  25 qed-.
  26
  27 lemma lreq_dropable: ∀RN,RP. dropable_dx (lexs RN RP).
  28 @lexs_dropable qed-.
  29
  30 (* Basic_2A1: includes: lreq_drop_trans_be *)
  31 lemma lreq_drops_trans_next: ∀L1,L2,f2. L1 ≡[f2] L2 →
  32                              ∀I,K2,V,c,f. ⬇*[c,f] L2 ≡ K2.ⓑ{I}V → 𝐔⦃f⦄ →
  33                              ∀f1. f ⊚ ⫯f1 ≡ f2 →
  34                              ∃∃K1. ⬇*[c,f] L1 ≡ K1.ⓑ{I}V & K1 ≡[f1] K2.
  35 #L1 #L2 #f2 #HL12 #I #K1 #V #c #f #HLK1 #Hf #f1 #Hf2
  36 elim (lexs_drops_trans_next … HL12 … HLK1 Hf … Hf2) -L2 -f2 -Hf
  37 /2 width=3 by ex2_intro/
  38 qed-.
  39
  40 (* Basic_2A1: includes: lreq_drop_conf_be *)
  41 lemma lreq_drops_conf_next: ∀L1,L2,f2. L1 ≡[f2] L2 →
  42                             ∀I,K1,V,c,f. ⬇*[c,f] L1 ≡ K1.ⓑ{I}V → 𝐔⦃f⦄ →
  43                             ∀f1. f ⊚ ⫯f1 ≡ f2 →
  44                             ∃∃K2. ⬇*[c,f] L2 ≡ K2.ⓑ{I}V & K1 ≡[f1] K2.
  45 #L1 #L2 #f2 #HL12 #I #K1 #V #c #f #HLK1 #Hf #f1 #Hf2
  46 elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -L1 -f2 -Hf
  47 /3 width=3 by lreq_sym, ex2_intro/
  48 qed-.
  49
  50 lemma drops_lreq_trans_next: ∀K1,K2,f1. K1 ≡[f1] K2 →
  51                              ∀I,L1,V,c,f. ⬇*[c,f] L1.ⓑ{I}V ≡ K1 →
  52                              ∀f2. f ⊚ f1 ≡ ⫯f2 →
  53                              ∃∃L2. ⬇*[c,f] L2.ⓑ{I}V ≡ K2 & L1 ≡[f2] L2 & L1.ⓑ{I}V≡[f]L2.ⓑ{I}V.
  54 #K1 #K2 #f1 #HK12 #I #L1 #V #c #f #HLK1 #f2 #Hf2
  55 elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -K1 -f1
  56 /2 width=6 by cfull_lift, ceq_lift, cfull_refl, ceq_refl, ex3_intro/
  57 qed-.