(* Forward lemmas with generic slicing for local environments ***************)
(* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
-lemma lsubr_fwd_drops2_bind: âL1,L2. L1 ⍠L2 â
- âb,f,I,K2. đâŚf⌠â âŹ*[b, f] L2 â K2.â{I} â
- â¨â¨ ââK1. K1 ⍠K2 & âŹ*[b, f] L1 â K1.â{I}
- | ââK1,W,V. K1 ⍠K2 & âŹ*[b, f] L1 â K1.ââW.V & I = BPair Abst W
- | ââJ1,J2,K1,V. K1 ⍠K2 & âŹ*[b, f] L1 â K1.â{J1}V & I = BUnit J2.
+lemma lsubr_fwd_drops2_bind:
+ âL1,L2. L1 ⍠L2 â
+ âb,f,I,K2. đâŚf⌠â âŠ*[b,f] L2 â K2.â{I} â
+ â¨â¨ ââK1. K1 ⍠K2 & âŠ*[b,f] L1 â K1.â{I}
+ | ââK1,W,V. K1 ⍠K2 & âŠ*[b,f] L1 â K1.ââW.V & I = BPair Abst W
+ | ââJ1,J2,K1,V. K1 ⍠K2 & âŠ*[b,f] L1 â K1.â{J1}V & I = BUnit J2.
#L1 #L2 #H elim H -L1 -L2
[ #b #f #I #K2 #_ #H
elim (drops_inv_atom1 ⌠H) -H #H destruct
qed-.
(* Basic_2A1: includes: lsubr_fwd_drop2_abbr *)
-lemma lsubr_fwd_drops2_abbr: âL1,L2. L1 ⍠L2 â
- âb,f,K2,V. đâŚf⌠â âŹ*[b, f] L2 â K2.âV â
- ââK1. K1 ⍠K2 & âŹ*[b, f] L1 â K1.âV.
+lemma lsubr_fwd_drops2_abbr:
+ âL1,L2. L1 ⍠L2 â
+ âb,f,K2,V. đâŚf⌠â âŠ*[b,f] L2 â K2.âV â
+ ââK1. K1 ⍠K2 & âŠ*[b,f] L1 â K1.âV.
#L1 #L2 #HL12 #b #f #K2 #V #Hf #HLK2
elim (lsubr_fwd_drops2_bind ⌠HL12 ⌠Hf HLK2) -L2 -Hf // *
[ #K1 #W #V #_ #_ #H destruct