matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_constructors.etc

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  14
  15 include "delayed_updating/unwind3/unwind_prototerm_eq.ma".
  16 include "delayed_updating/syntax/prototerm_constructors.ma".
  17 include "delayed_updating/relocation/sbr_push_uni.ma".
  18
  19 (* UNWIND FOR PROTOTERM *****************************************************)
  20
  21 (* Constructions with constructors for prototerm ****************************)
  22
  23 lemma unwind_iref_sn (f) (t:prototerm) (n:pnat):
  24       ▼[f❘@❨n❩⫯❘f]t ⊆ ▼[f](𝛗n.t).
  25 #f #t #n #p * #q #Hq #H0 destruct
  26 @(ex2_intro … (𝗱n◗𝗺◗q))
  27 /2 width=1 by in_comp_iref/
  28 qed-.
  29
  30 lemma unwind_iref_dx (f) (t) (n:pnat):
  31       ▼[f](𝛗n.t) ⊆ ▼[f❘@❨n❩⫯❘f]t.
  32 #f #t #n #p * #q #Hq #H0 destruct
  33 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  34 /2 width=1 by in_comp_unwind_bi/
  35 qed-.
  36
  37 lemma unwind_iref (f) (t) (n:pnat):
  38       ▼[f❘@❨n❩⫯❘f]t ⇔ ▼[f](𝛗n.t).
  39 /3 width=1 by conj, unwind_iref_sn, unwind_iref_dx/
  40 qed.
  41
  42 lemma unwind_iref_id (t) (n:pnat):
  43       ▼[𝐮❨n❩]t ⇔ ▼[𝐢](𝛗n.t).
  44 // qed.