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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  14
  15 include "basic_2/static/lsubr.ma".
  16 include "basic_2/rt_transition/cpg.ma".
  17
  18 (* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************)
  19
  20 (* Properties with restricted refinement for local environments *************)
  21
  22 lemma lsubr_cpg_trans: ∀h,r,G. lsub_trans … (cpg h r G) lsubr.
  23 #h #r #G #L1 #T1 #T2 #H elim H -r -G -L1 -T1 -T2
  24 [ //
  25 | /2 width=2 by cpg_st/
  26 | #r #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
  27   elim (lsubr_inv_abbr2 … H) -H #L2 #HL21 #H destruct
  28   /3 width=3 by cpg_delta/
  29 | #r #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
  30   elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
  31   /4 width=3 by cpg_delta, cpg_lt, cpg_ct/
  32 | #r #I1 #G #L1 #V1 #T1 #U1 #i #_ #HTU1 #IH #X #H
  33   elim (lsubr_fwd_pair2 … H) -H #I2 #L2 #V2 #HL21 #H destruct
  34   /3 width=3 by cpt_lref/
  35 |6,11: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/
  36 |7,9,10: /3 width=1 by cpg_flat, cpg_eps, cpg_ct/
  37 |8,12: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/
  38 ]
  39 qed-.