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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.