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

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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 EXTENDED PARALLEL RT-TRANSITION ***********)
  19
  20 (* Properties with simple terms *********************************************)
  21
  22 lemma csx_appl_simple (G) (L):
  23       ∀V. ❪G,L❫ ⊢ ⬈*𝐒 V → ∀T1.
  24       (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒 ⓐV.T2) →
  25       𝐒❪T1❫ → ❪G,L❫ ⊢ ⬈*𝐒 ⓐV.T1.
  26 #G #L #V #H @(csx_ind … H) -V
  27 #V #_ #IHV #T1 #IHT1 #HT1
  28 @csx_intro #X #H1 #H2
  29 elim (cpx_inv_appl1_simple … H1) // -H1
  30 #V0 #T0 #HLV0 #HLT10 #H destruct
  31 elim (tneqx_inv_pair … H2) -H2
  32 [ #H elim H -H //
  33 | #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
  34   @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
  35 | -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/
  36 ]
  37 qed.