- we set up the support for the "bt-reduction" of Automath literature

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / ysteps.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/ysteps.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/ysteps.ma
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/substitution/csup.ma".
+include "basic_2/computation/yprs.ma".
+
+(* ITERATED STEP OF HYPER PARALLEL COMPUTATION ON CLOSURES ******************)
+
+inductive ysteps (h) (g) (L1) (T1) (L2) (T2): Prop ≝
+| ysteps_intro: h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → (L1 = L2 → T1 = T2 → ⊥) →
+                ysteps h g L1 T1 L2 T2
+.
+
+interpretation "iterated step of hyper parallel computation (closure)"
+   'YPRedStepStar h g L1 T1 L2 T2 = (ysteps h g L1 T1 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma ssta_ysteps: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U →
+                   h ⊢ ⦃L, T⦄ •⭃*[g] ⦃L, U⦄.
+#h #g #L #T #U #l #HTU
+@ysteps_intro /3 width=2/ #_ #H destruct
+elim (ssta_inv_refl … HTU)
+qed.
+
+lemma csup_ysteps: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
+                   h ⊢ ⦃L1, T1⦄ •⭃*[g] ⦃L2, T2⦄.
+#h #g #L1 #L2 #T1 #T2 #H
+lapply (csup_fwd_cw … H) #H1
+@ysteps_intro /3 width=1/ -H #H2 #H3 destruct
+elim (lt_refl_false … H1)
+qed.