matita/matita/contribs/lambdadelta/basic_2/static/lsubr_drops.ma

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  14
  15 include "basic_2/relocation/drops.ma".
  16 include "basic_2/static/lsubr.ma".
  17
  18 (* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
  19
  20 (* Forward lemmas with generic slicing for local environments ***************)
  21
  22 (* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
  23 lemma lsubr_fwd_drops2_bind: ∀L1,L2. L1 ⫃ L2 →
  24                              ∀b,f,I,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2.ⓘ{I} →
  25                              ∨∨ ∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓘ{I}
  26                               | ∃∃K1,W,V. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
  27                               | ∃∃J1,J2,K1,V. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓑ{J1}V & I = BUnit J2.
  28 #L1 #L2 #H elim H -L1 -L2
  29 [ #b #f #I #K2 #_ #H
  30   elim (drops_inv_atom1 … H) -H #H destruct
  31 | #J #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V1
  32 ]
  33 #HL12 #IH #b #f #I #K2 #Hf #H
  34 elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
  35 [1,3,5: #Hf #H destruct -IH
  36   /4 width=6 by drops_refl, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
  37 |2,4,6: #g #Hg #HLK2 #H destruct -HL12
  38   elim (IH … Hg HLK2) -IH -Hg -HLK2 *
  39   /4 width=6 by drops_drop, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
  40 ]
  41 qed-.
  42
  43 (* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
  44 lemma lsubr_fwd_drops2_abbr: ∀L1,L2. L1 ⫃ L2 →
  45                              ∀b,f,K2,V.  𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2.ⓓV →
  46                              ∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≘ K1.ⓓV.
  47 #L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
  48 elim (lsubr_fwd_drops2_bind … HL12 … Hf HLK2) -L2 -Hf // *
  49 [ #K1 #W #V #_ #_ #H destruct
  50 | #I1 #I2 #K1 #V #_ #_ #H destruct
  51 ]
  52 qed-.