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basic_2: stronger supclosure allows better inversion lemmas
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14
15 include "basic_2/relocation/lreq.ma".
16 include "basic_2/static/frees.ma".
17
18 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
19
20 (* Properties with ranged equivalence for local environments ****************)
21
22 lemma frees_lreq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f → ∀L2. L1 ≡[f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
23 #f #L1 #T #H elim H -f -L1 -T
24 [ #f #I #Hf #X #H lapply (lreq_inv_atom1 … H) -H
25   #H destruct /2 width=1 by frees_atom/
26 | #f #I #L1 #V1 #s #_ #IH #X #H elim (lreq_inv_push1 … H) -H
27   /3 width=1 by frees_sort/
28 | #f #I #L1 #V1 #_ #IH #X #H elim (lreq_inv_next1 … H) -H
29   /3 width=1 by frees_zero/
30 | #f #I #L1 #V1 #i #_ #IH #X #H elim (lreq_inv_push1 … H) -H
31   /3 width=1 by frees_lref/
32 | #f #I #L1 #V1 #l #_ #IH #X #H elim (lreq_inv_push1 … H) -H
33   /3 width=1 by frees_gref/
34 | /6 width=5 by frees_bind, lreq_inv_tl, sle_lreq_trans, sor_inv_sle_dx, sor_inv_sle_sn/
35 | /5 width=5 by frees_flat, sle_lreq_trans, sor_inv_sle_dx, sor_inv_sle_sn/
36 ]
37 qed-.
38
39 lemma lreq_frees_trans: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f → ∀L2. L2 ≡[f] L1 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
40 /3 width=3 by frees_lreq_conf, lreq_sym/ qed-.