matita/matita/contribs/lambdadelta/ground/etc/relocation/pstream.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/notation/functions/upspoon_1.ma".
  16 include "ground/lib/stream.ma".
  17 include "ground/arith/pnat.ma".
  18
  19 (* RELOCATION P-STREAM ******************************************************)
  20
  21 (* Basic inversion lemmas ***************************************************)
  22
  23 lemma eq_inv_gr_push_bi: injective ? ? gr_push.
  24 #f1 #f2 <gr_push_unfold <gr_push_unfold #H destruct //
  25 qed-.
  26
  27 lemma eq_inv_gr_push_next: ∀f1,f2. ⫯f1 = ↑f2 → ⊥.
  28 #f1 * #p2 #f2 <gr_push_unfold <gr_next_unfold #H destruct
  29 qed-.
  30
  31 lemma eq_inv_gr_next_push: ∀f1,f2. ↑f1 = ⫯f2 → ⊥.
  32 * #p1 #f1 #f2 <gr_next_unfold <gr_push_unfold #H destruct
  33 qed-.
  34
  35 lemma eq_inv_gr_next_bi: injective ? ? gr_next.
  36 * #p1 #f1 * #p2 #f2 <gr_next_unfold <gr_next_unfold #H destruct //
  37 qed-.
  38
  39 lemma case_prop (Q:predicate gr_map):
  40       (∀f. Q (⫯f)) → (∀f. Q (↑f)) → ∀f. Q f.
  41 #Q #H1 #H2 * * //
  42 qed-.
  43
  44 lemma case_type0 (Q:gr_map→Type[0]):
  45       (∀f. Q (⫯f)) → (∀f. Q (↑f)) → ∀f. Q f.
  46 #Q #H1 #H2 * * //
  47 qed-.
  48
  49 lemma iota_push: ∀Q,a,b,f. a f = case_type0 Q a b (⫯f).
  50 // qed.
  51
  52 lemma iota_next: ∀Q,a,b,f. b f = case_type0 Q a b (↑f).
  53 #Q #a #b * //
  54 qed.