matita/matita/contribs/lambdadelta/ground/relocation/gr_tl_eq_eq.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "ground/relocation/gr_tl_eq.ma".
  16
  17 (* TAIL FOR GENERIC RELOCATION MAPS *****************************************)
  18
  19 (* Main constructions with gr_eq ********************************************)
  20
  21 (*** eq_trans *)
  22 corec theorem gr_eq_trans: Transitive … gr_eq.
  23 #f1 #f * -f1 -f
  24 #f1 #f #g1 #g #Hf1 #H1 #H #f2 #Hf2
  25 [ cases (gr_eq_inv_push_sn … Hf2 … H)
  26 | cases (gr_eq_inv_next_sn … Hf2 … H)
  27 ] -g
  28 /3 width=5 by gr_eq_push, gr_eq_next/
  29 qed-.
  30
  31 (*** eq_canc_sn *)
  32 theorem gr_eq_canc_sn (f2): gr_eq_repl_back (λf. f ≡ f2).
  33 /3 width=3 by gr_eq_trans, gr_eq_sym/ qed-.
  34
  35 (*** eq_canc_dx *)
  36 theorem gr_eq_canc_dx (f1): gr_eq_repl_fwd (λf. f1 ≡ f).
  37 /3 width=5 by gr_eq_canc_sn, gr_eq_repl_sym/ qed-.