matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_aaa.ma

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  14
  15 include "basic_2/rt_computation/cpms_aaa.ma".
  16 include "basic_2/rt_equivalence/cpes.ma".
  17
  18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
  19
  20 (* Properties with atomic arity assignment on terms *************************)
  21
  22 (* Basic_2A1: uses: scpes_refl *)
  23 lemma cpes_refl_aaa (h) (n):
  24       ∀G,L,T,A.  ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ T ⬌*[h,n,n] T.
  25 #h #n #G #L #T #A #HA
  26 elim (aaa_cpms_total h … n … HA) #U #HTU
  27 /2 width=3 by cpms_div/
  28 qed.
  29
  30 (* Main inversion lemmas with atomic arity assignment on terms **************)
  31
  32 (* Basic_2A1: uses: scpes_aaa_mono *)
  33 theorem cpes_aaa_mono (h) (n1) (n2):
  34         ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h,n1,n2] T2 →
  35         ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 → A1 = A2.
  36 #h #n1 #n2 #G #L #T1 #T2 * #T #HT1 #HT2 #A1 #HA1 #A2 #HA2
  37 lapply (cpms_aaa_conf … HA1 … HT1) -T1 #HA1
  38 lapply (cpms_aaa_conf … HA2 … HT2) -T2 #HA2
  39 lapply (aaa_mono … HA1 … HA2) -L -T //
  40 qed-.