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14
15 include "static_2/relocation/drops.ma".
16 include "static_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:
24       âˆ€L1,L2. L1 âŤƒ L2 â†’
25       âˆ€b,f,I,K2. đ”❨f❊ â†’ â‡Š*[b,f] L2 â‰˜ K2.ⓘ[I] â†’
26       âˆ¨âˆ¨ âˆƒâˆƒK1. K1 âŤƒ K2 & â‡Š*[b,f] L1 â‰˜ K1.ⓘ[I]
27        | âˆƒâˆƒK1,W,V. K1 âŤƒ K2 & â‡Š*[b,f] L1 â‰˜ K1.ⓓⓝW.V & I = BPair Abst W
28        | âˆƒâˆƒJ1,J2,K1,V. K1 âŤƒ K2 & â‡Š*[b,f] L1 â‰˜ K1.ⓑ[J1]V & I = BUnit J2.
29 #L1 #L2 #H elim H -L1 -L2
30 [ #b #f #I #K2 #_ #H
31   elim (drops_inv_atom1 â€Ś H) -H #H destruct
32 | #J #L1 #L2 | #L1 #L2 #V #W | #I1 #I2 #L1 #L2 #V1
33 ]
34 #HL12 #IH #b #f #I #K2 #Hf #H
35 elim (drops_inv_bind1_isuni â€Ś Hf H) -Hf -H *
36 [1,3,5: #Hf #H destruct -IH
37   /4 width=6 by drops_refl, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
38 |2,4,6: #g #Hg #HLK2 #H destruct -HL12
39   elim (IH â€Ś Hg HLK2) -IH -Hg -HLK2 *
40   /4 width=6 by drops_drop, or3_intro0, or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro, ex2_intro/
41 ]
42 qed-.
43
44 (* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
45 lemma lsubr_fwd_drops2_abbr:
46       âˆ€L1,L2. L1 âŤƒ L2 â†’
47       âˆ€b,f,K2,V. đ”❨f❊ â†’ â‡Š*[b,f] L2 â‰˜ K2.ⓓV â†’
48       âˆƒâˆƒK1. K1 âŤƒ K2 & â‡Š*[b,f] L1 â‰˜ K1.ⓓV.
49 #L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
50 elim (lsubr_fwd_drops2_bind â€Ś HL12 â€Ś Hf HLK2) -L2 -Hf // *
51 [ #K1 #W #V #_ #_ #H destruct
52 | #I1 #I2 #K1 #V #_ #_ #H destruct
53 ]
54 qed-.