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

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   3 (*      ||M||                                                             *)
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  14
  15 include "ground/relocation/pr_after.ma".
  16
  17 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
  18
  19 corec definition pr_compose: pr_map → pr_map → pr_map.
  20 * * #g2 [ #f1 | * * #g1 ]
  21 [ @pr_next @(pr_compose g2 f1)
  22 | @pr_next @(pr_compose g2 g1)
  23 | @pr_push @(pr_compose g2 g1)
  24 ]
  25 defined.
  26
  27 interpretation
  28   "functional composition (partial relocation maps)"
  29   'compose f2 f1 = (pr_compose f2 f1).
  30
  31 (* Basic constructions (specific) *******************************************)
  32
  33 lemma pr_compose_unfold_refl (f2) (f1): ⫯(f2∘f1) = (⫯f2)∘(⫯f1).
  34 #f2 #f1
  35 <(stream_unfold … ((⫯f2)∘(⫯f1))) in ⊢ (???%); //
  36 qed.
  37
  38 lemma pr_compose_unfold_push (f2) (f1): ↑(f2∘f1) = (⫯f2)∘(↑f1).
  39 #f2 #f1
  40 <(stream_unfold … ((⫯f2)∘(↑f1))) in ⊢ (???%); //
  41 qed.
  42
  43 lemma pr_compose_unfold_next (f2) (f1):
  44       ↑(f2∘f1) = (↑f2)∘f1.
  45 #f2 #f1
  46 <(stream_unfold … ((↑f2)∘f1)) in ⊢ (???%); //
  47 qed.
  48
  49 (* Main constructions *******************************************************)
  50
  51 corec theorem pr_after_compose (f2) (f1):
  52               f2 ⊚ f1 ≘ f2∘f1.
  53 cases (pr_map_split_tl f2)*
  54 [ cases (pr_map_split_tl f1) * ]
  55 [ @pr_after_refl /2 width=7 by/
  56 | @pr_after_push /2 width=7 by/
  57 | @pr_after_next /2 width=5 by/
  58 ]
  59 qed.