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

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  14
  15 include "basic_2/rt_computation/cpms_aaa.ma".
  16 include "basic_2/rt_equivalence/cpcs_cprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
  19
  20 (* Main inversion lemmas with atomic arity assignment on terms **************)
  21
  22 (* Note: lemma 1500 *)
  23 theorem cpcs_aaa_mono (h) (G) (L): ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h] T2 →
  24                                    ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
  25                                    A1 = A2.
  26 #h #G #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
  27 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
  28 lapply (cpms_aaa_conf … HA1 … HT1) -T1 #HA1
  29 lapply (cpms_aaa_conf … HA2 … HT2) -T2 #HA2
  30 lapply (aaa_mono … HA1 … HA2) -L -T //
  31 qed-.