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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "delayed_updating/substitution/lift_prototerm_eq.ma".
16 include "delayed_updating/syntax/prototerm_constructors.ma".
18 (* LIFT FOR PROTOTERM *******************************************************)
20 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
21 (šf@āØnā©.ā[ā*[n]f]t) ā ā[f](šn.t).
22 #f #t #n #p * #q * #r #Hr #H1 #H2 destruct
23 @(ex2_intro ā¦ (š±nāšŗār))
24 /2 width=1 by in_comp_iref/
27 lemma lift_iref_dx (f) (t) (n:pnat):
28 ā[f](šn.t) ā šf@āØnā©.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/
34 lemma lift_iref (f) (t) (n:pnat):
35 (šf@āØnā©.ā[ā*[n]f]t) ā ā[f](šn.t).
36 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/