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

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  14
  15 include "static_2/syntax/theq_simple.ma".
  16 include "static_2/syntax/theq_theq.ma".
  17 include "basic_2/rt_transition/cpx_simple.ma".
  18 include "basic_2/rt_computation/cpxs.ma".
  19 include "basic_2/rt_computation/csx_csx.ma".
  20
  21 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
  22
  23 (* Properties with head equivalence for terms *******************************)
  24
  25 (* Basic_1: was just: sn3_appl_appl *)
  26 (* Basic_2A1: was: csx_appl_simple_tsts *)
  27 lemma csx_appl_simple_theq: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
  28                             (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T2⦄) →
  29                             𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T1⦄.
  30 #h #o #G #L #V #H @(csx_ind … H) -V
  31 #V #_ #IHV #T1 #H @(csx_ind … H) -T1
  32 #T1 #H1T1 #IHT1 #H2T1 #H3T1
  33 @csx_intro #X #HL #H
  34 elim (cpx_inv_appl1_simple … HL) -HL //
  35 #V0 #T0 #HLV0 #HLT10 #H0 destruct
  36 elim (tdneq_inv_pair … H) -H
  37 [ #H elim H -H //
  38 | -IHT1 #HV0
  39   @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
  40   @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
  41 | -IHV -H1T1 #H1T10
  42   @(csx_cpx_trans … (ⓐV.T0)) /2 width=1 by cpx_flat/ -HLV0
  43   elim (theq_dec h o T1 T0) #H2T10
  44   [ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, theq_canc_sn, simple_theq_repl_dx/
  45   | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
  46   ]
  47 ]
  48 qed.