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14
15 include "basic_2/relocation/drops_ceq.ma".
16 include "basic_2/relocation/drops_lexs.ma".
17
18 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
19
20 (* Properties with ranged equivalence for local environments ****************)
21
22 lemma lreq_co_dedropable: co_dedropable_sn lreq.
23 @lexs_liftable_co_dedropable
24 /2 width=6 by cfull_lift, ceq_lift/ qed-.
25
26 lemma lreq_co_dropable_sn: co_dropable_sn lreq.
27 @lexs_co_dropable_sn qed-.
28
29 lemma lreq_co_dropable_dx: co_dropable_dx lreq.
30 @lexs_co_dropable_dx qed-.
31
32 (* Basic_2A1: includes: lreq_drop_trans_be *)
33 lemma lreq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
34                              ∀b,f,I,K2,V. ⬇*[b,f] L2 ≡ K2.ⓑ{I}V → 𝐔⦃f⦄ →
35                              ∀f1. f ~⊚ ⫯f1 ≡ f2 →
36                              ∃∃K1. ⬇*[b,f] L1 ≡ K1.ⓑ{I}V & K1 ≡[f1] K2.
37 #f2 #L1 #L2 #HL12 #b #f #I #K1 #V #HLK1 #Hf #f1 #Hf2
38 elim (lexs_drops_trans_next … HL12 … HLK1 Hf … Hf2) -f2 -L2 -Hf
39 /2 width=3 by ex2_intro/
40 qed-.
41
42 (* Basic_2A1: includes: lreq_drop_conf_be *)
43 lemma lreq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
44                             ∀b,f,I,K1,V. ⬇*[b,f] L1 ≡ K1.ⓑ{I}V → 𝐔⦃f⦄ →
45                             ∀f1. f ~⊚ ⫯f1 ≡ f2 →
46                             ∃∃K2. ⬇*[b,f] L2 ≡ K2.ⓑ{I}V & K1 ≡[f1] K2.
47 #f2 #L1 #L2 #HL12 #b #f #I #K1 #V #HLK1 #Hf #f1 #Hf2
48 elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
49 /3 width=3 by lreq_sym, ex2_intro/
50 qed-.
51
52 lemma drops_lreq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
53                              ∀b,f,I,L1,V. ⬇*[b,f] L1.ⓑ{I}V ≡ K1 →
54                              ∀f2. f ~⊚ f1 ≡ ⫯f2 →
55                              ∃∃L2. ⬇*[b,f] L2.ⓑ{I}V ≡ K2 & L1 ≡[f2] L2 & L1.ⓑ{I}V ≡[f] L2.ⓑ{I}V.
56 #f1 #K1 #K2 #HK12 #b #f #I #L1 #V #HLK1 #f2 #Hf2
57 elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
58 /2 width=6 by cfull_lift, ceq_lift, ex3_intro/ qed-.