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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/static/frees_fqup.ma".
16 include "basic_2/static/lsubf_lsubr.ma".
17 include "basic_2/static/fle.ma".
19 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
21 (* Advanced forward lemmas ***************************************************)
23 lemma fle_fwd_pair_sn: ∀I1,I2,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
24 ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄.
25 #I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 *
26 #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12
27 elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
28 elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
29 lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
30 /5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)