matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cnv_cpmue.etc

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/cpms_cnu.ma".
  16 include "basic_2/rt_computation/cpmue.ma".
  17 include "basic_2/dynamic/cnv_preserve.ma".
  18
  19 (* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
  20
  21 (* Properties with evaluation for t-unbound rt-transition on terms **********)
  22
  23 lemma cnv_cpmue_trans (a) (h) (G) (L):
  24       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
  25       ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
  26 /3 width=4 by cpmue_fwd_cpms, cnv_cpms_trans/ qed-.
  27
  28 lemma cnv_cpmue_cpms_conf (a) (h) (G) (L):
  29       ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[n1,h] T1 →
  30       ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ →
  31       ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[h,n2-n1] 𝐍*⦃T⦄ & T2 ≅ T.
  32 #a #h #G #L #T0 #HT0 #T1 #n1 #HT01 #T2 #n2 * #HT02 #HT2
  33 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  34 lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
  35 /4 width=8 by cpmue_intro, cnu_tueq_trans, ex2_intro/
  36 qed-.
  37
  38 (* Main properties with evaluation for t-unbound rt-transition on terms *****)
  39
  40 theorem cnv_cpmue_mono (a) (h) (G) (L):
  41         ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[h,n1] 𝐍*⦃T1⦄ →
  42         ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ → T1 ≅ T2.
  43 #a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
  44 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  45 /3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/
  46 qed-.