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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "static_2/s_computation/fqus.ma".
16 include "basic_2/rt_computation/csx_lsubr.ma".
18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
20 (* Properties with extended supclosure **************************************)
22 lemma csx_fqu_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
23 ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
24 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
25 [ /3 width=5 by csx_inv_lref_pair, drops_refl/
26 | /2 width=3 by csx_fwd_pair_sn/
27 | /2 width=2 by csx_fwd_bind_dx/
28 | /2 width=4 by csx_fwd_bind_dx_unit/
29 | /2 width=3 by csx_fwd_flat_dx/
30 | /4 width=7 by csx_inv_lifts, drops_refl, drops_drop/
34 lemma csx_fquq_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
35 ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
36 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=6 by csx_fqu_conf/
37 * #HG #HL #HT destruct //
40 lemma csx_fqup_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
41 ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
42 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
43 /3 width=6 by csx_fqu_conf/
46 lemma csx_fqus_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
47 ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
48 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -H
49 /3 width=6 by csx_fquq_conf/