matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind1/unwind_constructors.etc

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  14
  15 include "delayed_updating/unwind1/unwind_prototerm_eq.ma".
  16 include "delayed_updating/syntax/prototerm_constructors.ma".
  17
  18 (* UNWIND FOR PROTOTERM *****************************************************)
  19
  20 lemma unwind_iref_sn (f) (t:prototerm) (n:pnat):
  21       ▼[𝐮❨f＠⧣❨n❩❩]t ⊆ ▼[f](𝛗n.t).
  22 #f #t #n #p * #q #Hq #H0 destruct
  23 @(ex2_intro … (𝗱n◗𝗺◗q))
  24 /2 width=1 by in_comp_iref/
  25 qed-.
  26
  27 lemma unwind_iref_dx (f) (t) (n:pnat):
  28       ▼[f](𝛗n.t) ⊆ ▼[𝐮❨f＠⧣❨n❩❩]t.
  29 #f #t #n #p * #q #Hq #H0 destruct
  30 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  31 /2 width=1 by in_comp_unwind_bi/
  32 qed-.
  33
  34 lemma unwind_iref (f) (t) (n:pnat):
  35       ▼[𝐮❨f＠⧣❨n❩❩]t ⇔ ▼[f](𝛗n.t).
  36 /3 width=1 by conj, unwind_iref_sn, unwind_iref_dx/
  37 qed.