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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_bind: âL1,L2. L1 ⍠L2 â
24 âb,f,I,K2. đâŚf⌠â âŹ*[b, f] L2 â K2.â{I} â
25 â¨â¨ ââK1. K1 ⍠K2 & âŹ*[b, f] L1 â K1.â{I}
26 | ââK1,W,V. K1 ⍠K2 & âŹ*[b, f] L1 â K1.ââW.V & I = BPair Abst W
27 | ââJ1,J2,K1,V. K1 ⍠K2 & âŹ*[b, f] L1 â K1.â{J1}V & I = BUnit J2.
28 #L1 #L2 #H elim H -L1 -L2
30 elim (drops_inv_atom1 ⌠H) -H #H destruct
31 | #J #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V1
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/
43 (* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
44 lemma lsubr_fwd_drops2_abbr: âL1,L2. L1 ⍠L2 â
45 âb,f,K2,V. đâŚf⌠â âŹ*[b, f] L2 â K2.âV â
46 ââK1. K1 ⍠K2 & âŹ*[b, f] L1 â K1.âV.
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