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

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   3 (*      ||M||                                                             *)
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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 include "ground/relocation/gr_sor.ma".
  17
  18 (* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
  19
  20 (* Constructions with gr_eq *************************************************)
  21
  22 (*** sor_eq_repl_back1 *)
  23 corec lemma gr_sor_eq_repl_back_sn:
  24             ∀f2,f. gr_eq_repl_back … (λf1. f1 ⋓ f2 ≘ f).
  25 #f2 #f #f1 * -f1 -f2 -f
  26 #f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x #Hx
  27 try cases (gr_eq_inv_push_sn … Hx … H1) try cases (gr_eq_inv_next_sn … Hx … H1) -g1
  28 /3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
  29 qed-.
  30
  31 (*** sor_eq_repl_fwd1 *)
  32 lemma gr_sor_eq_repl_fwd_sn:
  33       ∀f2,f. gr_eq_repl_fwd … (λf1. f1 ⋓ f2 ≘ f).
  34 #f2 #f @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back_sn/
  35 qed-.
  36
  37 (*** sor_eq_repl_back2 *)
  38 corec lemma gr_sor_eq_repl_back_dx:
  39             ∀f1,f. gr_eq_repl_back … (λf2. f1 ⋓ f2 ≘ f).
  40 #f1 #f #f2 * -f1 -f2 -f
  41 #f1 #f2 #f #g1 #g2 #g #Hf #H #H2 #H0 #x #Hx
  42 try cases (gr_eq_inv_push_sn … Hx … H2) try cases (gr_eq_inv_next_sn … Hx … H2) -g2
  43 /3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
  44 qed-.
  45
  46 (*** sor_eq_repl_fwd2 *)
  47 lemma gr_sor_eq_repl_fwd_dx:
  48       ∀f1,f. gr_eq_repl_fwd … (λf2. f1 ⋓ f2 ≘ f).
  49 #f1 #f @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back_dx/
  50 qed-.
  51
  52 (*** sor_eq_repl_back3 *)
  53 corec lemma gr_sor_eq_repl_back:
  54             ∀f1,f2. gr_eq_repl_back … (λf. f1 ⋓ f2 ≘ f).
  55 #f1 #f2 #f * -f1 -f2 -f
  56 #f1 #f2 #f #g1 #g2 #g #Hf #H #H2 #H0 #x #Hx
  57 try cases (gr_eq_inv_push_sn … Hx … H0) try cases (gr_eq_inv_next_sn … Hx … H0) -g
  58 /3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
  59 qed-.
  60
  61 (*** sor_eq_repl_fwd3 *)
  62 lemma gr_sor_eq_repl_fwd:
  63       ∀f1,f2. gr_eq_repl_fwd … (λf. f1 ⋓ f2 ≘ f).
  64 #f1 #f2 @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back/
  65 qed-.