matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_simple.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/syntax/term_simple.ma".
  16 include "basic_2/rt_transition/cpg.ma".
  17
  18 (* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
  19
  20 (* Properties with simple terms *********************************************)
  21
  22 (* Note: the main property of simple terms *)
  23 lemma cpg_inv_appl1_simple: ∀Rt,c,h,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ⬈[Rt, c, h] U → 𝐒⦃T1⦄ →
  24                             ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⦃G, L⦄ ⊢ T1 ⬈[Rt, cT, h] T2 &
  25                                            U = ⓐV2.T2 & c = ((↕*cV)∨cT).
  26 #Rt #c #h #G #L #V1 #T1 #U #H #HT1 elim (cpg_inv_appl1 … H) -H *
  27 [ /2 width=8 by ex4_4_intro/
  28 | #cV #cW #cT #p #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H destruct
  29   elim (simple_inv_bind … HT1)
  30 | #cV #cW #cT #p #V #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #_ #H destruct
  31   elim (simple_inv_bind … HT1)
  32 ]
  33 qed-.