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

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/rt_transition/cpx_simple.ma".
  16 include "basic_2/rt_computation/csx_csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
  19
  20 (* Properties with simple terms *********************************************)
  21
  22 lemma csx_appl_simple: ∀h,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ∀T1.
  23                        (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T2⦄) →
  24                        𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T1⦄.
  25 #h #G #L #V #H @(csx_ind … H) -V
  26 #V #_ #IHV #T1 #IHT1 #HT1
  27 @csx_intro #X #H1 #H2
  28 elim (cpx_inv_appl1_simple … H1) // -H1
  29 #V0 #T0 #HLV0 #HLT10 #H destruct
  30 elim (tdneq_inv_pair … H2) -H2
  31 [ #H elim H -H //
  32 | #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
  33   @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
  34 | -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/
  35 ]
  36 qed.