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

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  14
  15 include "basic_2/rt_transition/lfpx_lfdeq.ma".
  16 include "basic_2/rt_computation/cpxs.ma".
  17
  18 (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
  19
  20 (* Properties with degree-based equivalence for terms ***********************)
  21
  22 lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≛[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
  23                        ∃∃U2.  ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛[h, o] T2.
  24 #h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
  25 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
  26 /3 width=3 by ex2_intro, cpxs_strap1/
  27 qed-.
  28
  29 (* Note: this requires tdeq to be symmetric *)
  30 lemma cpxs_tdneq_inv_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) →
  31                               ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛[h, o] T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛[h, o] T2.
  32 #h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
  33 [ #H elim H -H //
  34 | #T1 #T #H1 #H2 #IH #Hn12 elim (tdeq_dec h o T1 T) #H destruct
  35   [ -H1 -H2 elim IH -IH /3 width=3 by tdeq_trans/ -Hn12
  36     #X #X2 #HTX #HnTX #HX2 #HXT2 elim (tdeq_cpx_trans … H … HTX) -HTX
  37     #X1 #HTX1 #HX1 elim (tdeq_cpxs_trans … HX1 … HX2) -HX2
  38     /5 width=8 by tdeq_canc_sn, tdeq_trans, ex4_2_intro/ (* Note: 2 tdeq_trans *)
  39   | -IH -Hn12 /3 width=6 by ex4_2_intro/
  40   ]
  41 ]
  42 qed-.