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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/lfxs_length.ma".
16 include "basic_2/rt_transition/lfpx.ma".
18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
20 (* Forward lemmas with length for local environments ************************)
22 lemma lfpx_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → |L1| = |L2|.
23 /2 width=3 by lfxs_fwd_length/ qed-.
25 (* Inversion lemmas with length for local environments **********************)
27 lemma lfpx_inv_zero_length: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
29 | ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
30 ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
31 Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
32 |∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
33 /2 width=1 by lfxs_inv_zero_length/ qed-.