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14
15 include "delayed_updating/substitution/lift_prototerm_eq.ma".
16 include "delayed_updating/syntax/prototerm_constructors.ma".
17
18 (* LIFT FOR PROTOTERM *******************************************************)
19
20 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
21       (š›—f@āØnā©.ā†‘[ā‡‚*[n]f]t) āŠ† ā†‘[f](š›—n.t).
22 #f #t #n #p * #q * #r #Hr #H1 #H2 destruct
23 @(ex2_intro ā€¦ (š—±nā——š—ŗā——r))
24 /2 width=1 by in_comp_iref/
25 qed-.
26
27 lemma lift_iref_dx (f) (t) (n:pnat):
28       ā†‘[f](š›—n.t) āŠ† š›—f@āØnā©.ā†‘[ā‡‚*[n]f]t.
29 #f #t #n #p * #q #Hq #H0 destruct
30 elim (in_comp_inv_iref ā€¦ Hq) -Hq #p #H0 #Hp destruct
31 /3 width=1 by in_comp_iref, in_comp_lift_bi/
32 qed-.
33
34 lemma lift_iref (f) (t) (n:pnat):
35       (š›—f@āØnā©.ā†‘[ā‡‚*[n]f]t) ā‡” ā†‘[f](š›—n.t).
36 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
37 qed.