matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fpbc.ma

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   3 (*      ||M||                                                             *)
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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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  14
  15 include "basic_2/rt_transition/fpbc_feqg.ma".
  16 include "basic_2/rt_transition/fpbc_fpb.ma".
  17 include "basic_2/rt_computation/fpbs_feqg.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Properties with proper parallel rst-reduction on closures ****************)
  22
  23 lemma fpbc_fpbs:
  24       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
  25       ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  26 /3 width=1 by fpb_fpbs, fpbc_fwd_fpb/ qed.
  27
  28 (* Inversion lemmas with proper parallel rst-reduction on closures **********)
  29
  30 lemma fpbs_inv_fpbc_sn:
  31       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ →
  32       ∨∨ ❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫
  33        | ∃∃G,L,T. ❪G1,L1,T1❫ ≻ ❪G,L,T❫ & ❪G,L,T❫ ≥ ❪G2,L2,T2❫.
  34 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
  35 [ /3 width=1 by feqg_refl, or_introl/
  36 | #G #G2 #L #L2 #T #T2 #_ #H2 * [ #H1 | * #G0 #L0 #T0 #H10 #H0 ]
  37   elim (fpb_inv_fpbc … H2) -H2 #H2
  38   [ /3 width=5 by feqg_trans, or_introl/
  39   | lapply (feqg_fpbc_trans … H1 … H2) -G -L -T //
  40     /3 width=5 by fpb_fpbs, ex2_3_intro, or_intror/
  41   | /4 width=12 by fpbs_feqg_trans, ex2_3_intro, or_intror/
  42   | /5 width=9 by fpbs_strap1, fpbc_fwd_fpb, ex2_3_intro, or_intror/
  43   ]
  44 ]
  45 qed-.