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

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  14
  15 include "basic_2/rt_transition/lpx.ma".
  16 include "basic_2/rt_computation/cpxs_drops.ma".
  17 include "basic_2/rt_computation/cpxs_cpxs.ma".
  18
  19 (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
  20
  21 (* Properties with uncounted parallel rt-transition for local environments **)
  22
  23 lemma lpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (λ_.lpx h G).
  24 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2
  25 [ /2 width=3 by/
  26 | /3 width=2 by cpx_cpxs, cpx_ess/
  27 | #I #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
  28   elim (lpx_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
  29   /4 width=3 by cpxs_delta, cpxs_strap2/
  30 | #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
  31   elim (lpx_inv_bind_dx … H) -H #I1 #K1 #HK12 #HI12 #H destruct
  32   /4 width=3 by cpxs_lref, cpxs_strap2/
  33 |5,10: /4 width=1 by cpxs_beta, cpxs_bind, lpx_bind_refl_dx/
  34 |6,8,9: /3 width=1 by cpxs_flat, cpxs_ee, cpxs_eps/
  35 | /4 width=3 by cpxs_zeta, lpx_bind_refl_dx/
  36 | /4 width=3 by cpxs_theta, cpxs_strap1, lpx_bind_refl_dx/
  37 ]
  38 qed-.
  39
  40 lemma lpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (λ_.lpx h G).
  41 #h #G @s_r_trans_LTC1 /2 width=3 by lpx_cpx_trans/ (**) (* full auto fails *)
  42 qed-.