matita/matita/contribs/lambdadelta/static_2/syntax/theq_simple.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "static_2/syntax/term_simple.ma".
  16 include "static_2/syntax/theq.ma".
  17
  18 (* HEAD EQUIVALENCE FOR TERMS ***********************************************)
  19
  20 (* Properies with simple (neutral) terms ************************************)
  21
  22 (* Basic_2A1: was: simple_tsts_repl_dx *)
  23 lemma simple_theq_repl_dx: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
  24 #T1 #T2 * -T1 -T2 //
  25 #I #V1 #V2 #T1 #T2 #H
  26 elim (simple_inv_pair … H) -H #J #H destruct //
  27 qed-.
  28
  29 (* Basic_2A1: was: simple_tsts_repl_sn *)
  30 lemma simple_theq_repl_sn: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
  31 /3 width=3 by simple_theq_repl_dx, theq_sym/ qed-.