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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/relocation/drops.ma".
16 include "basic_2/static/lsubr.ma".
18 (* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
20 (* Forward lemmas with generic slicing for local environments ***************)
22 (* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
23 lemma lsubr_fwd_drops2_pair: ∀L1,L2. L1 ⫃ L2 →
24 ∀b,f,I,K2,W. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≡ K2.ⓑ{I}W →
25 (∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≡ K1.ⓑ{I}W) ∨
26 ∃∃K1,V. K1 ⫃ K2 & ⬇*[b, f] L1 ≡ K1.ⓓⓝW.V & I = Abst.
27 #L1 #L2 #H elim H -L1 -L2
28 [ #L #b #f #I #K2 #W #_ #H
29 elim (drops_inv_atom1 … H) -H #H destruct
30 | #J #L1 #L2 #V #HL12 #IH #b #f #I #K2 #W #Hf #H
31 elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
33 /4 width=4 by drops_refl, ex2_intro, or_introl/
34 | #g #Hg #HLK2 #H destruct -HL12
35 elim (IH … Hg HLK2) -IH -Hg -HLK2 *
36 /4 width=4 by drops_drop, ex3_2_intro, ex2_intro, or_introl, or_intror/
38 | #L1 #L2 #V1 #V2 #HL12 #IH #b #f #I #K2 #W #Hf #H
39 elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
41 /4 width=4 by drops_refl, ex3_2_intro, or_intror/
42 | #g #Hg #HLK2 #H destruct -HL12
43 elim (IH … Hg HLK2) -IH -Hg -HLK2 *
44 /4 width=4 by drops_drop, ex3_2_intro, ex2_intro, or_introl, or_intror/
49 (* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
50 lemma lsubr_fwd_drops2_abbr: ∀L1,L2. L1 ⫃ L2 →
51 ∀b,f,K2,V. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≡ K2.ⓓV →
52 ∃∃K1. K1 ⫃ K2 & ⬇*[b, f] L1 ≡ K1.ⓓV.
53 #L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
54 elim (lsubr_fwd_drops2_pair … HL12 … Hf HLK2) -L2 -Hf // *
55 #K1 #W #_ #_ #H destruct