1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 (* Advanced properties ******************************************************)
17 lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
18 ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2.
19 #h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
20 [ /3 width=3 by cpxs_sort, da_inv_sort/
21 | #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
22 elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
23 lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpxs_delta/
24 | #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
25 elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
26 lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
27 #HV1 #H destruct lapply (le_plus_to_le_c … Hd21) -Hd21
28 /3 width=7 by cpxs_delta/
29 | /4 width=3 by cpxs_bind_dx, da_inv_bind/
30 | /4 width=3 by cpxs_flat_dx, da_inv_flat/
31 | /4 width=3 by cpxs_eps, da_inv_flat/
35 lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
36 ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
37 ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
38 ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
39 /3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-.
41 lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
42 ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
43 ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
44 ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
45 /3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-.