matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_aaa.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       *)
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  14
  15 include "basic_2/computation/fprs_aaa.ma".
  16 include "basic_2/equivalence/fpcs_fpcs.ma".
  17
  18 (* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
  19
  20 (* Main properties about atomic arity assignment on terms *******************)
  21
  22 theorem aaa_fpcs_mono: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ →
  23                        ∀A1. L1 ⊢ T1 ⁝ A1 → ∀A2. L2 ⊢ T2 ⁝ A2 →
  24                        A1 = A2.
  25 #L1 #L2 #T1 #T2 #H12 #A1 #HT1 #A2 #HT2
  26 elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
  27 lapply (aaa_fprs_conf … HT1 … H1) -L1 -T1 #HT1
  28 lapply (aaa_fprs_conf … HT2 … H2) -L2 -T2 #HT2
  29 lapply (aaa_mono … HT1 … HT2) -L -T //
  30 qed-.