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 notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⭃ * break [ g ] break ⦃ L2 , break T2 ⦄ )"
16 non associative with precedence 45
17 for @{ 'YPRedStepStar $h $g $L1 $T1 $L2 $T2 }.
19 include "basic_2/substitution/csup.ma".
20 include "basic_2/computation/yprs.ma".
22 (* ITERATED STEP OF HYPER PARALLEL COMPUTATION ON CLOSURES ******************)
24 inductive ysteps (h) (g) (L1) (T1) (L2) (T2): Prop ≝
25 | ysteps_intro: h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → (L1 = L2 → T1 = T2 → ⊥) →
26 ysteps h g L1 T1 L2 T2
29 interpretation "iterated step of hyper parallel computation (closure)"
30 'YPRedStepStar h g L1 T1 L2 T2 = (ysteps h g L1 T1 L2 T2).
32 (* Basic properties *********************************************************)
34 lemma ssta_ysteps: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U →
35 h ⊢ ⦃L, T⦄ •⭃*[g] ⦃L, U⦄.
36 #h #g #L #T #U #l #HTU
37 @ysteps_intro /3 width=2/ #_ #H destruct
38 elim (ssta_inv_refl … HTU)
41 lemma csup_ysteps: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
42 h ⊢ ⦃L1, T1⦄ •⭃*[g] ⦃L2, T2⦄.
43 #h #g #L1 #L2 #T1 #T2 #H
44 lapply (csup_fwd_cw … H) #H1
45 @ysteps_intro /3 width=1/ -H #H2 #H3 destruct
46 elim (lt_refl_false … H1)