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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/substitution/lift_uni.ma".
17 include "delayed_updating/syntax/prototerm_constructors.ma".
19 (* LIFT FOR PROTOTERM *******************************************************)
21 lemma lift_iref_bi (t1) (t2) (n):
22 t1 ⇔ t2 → 𝛗n.t1 ⇔ 𝛗n.t2.
23 /2 width=1 by subset_equivalence_ext_f1_bi/
26 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
27 (𝛗f@❨n❩.t) ⊆ ↑[f](𝛗n.t).
28 #f #t #n #p * #q #Hq #H0 destruct
29 @(ex2_intro … (𝗱n◗𝗺◗q))
30 /2 width=1 by in_comp_iref/
33 lemma lift_iref_dx (f) (t) (n:pnat):
34 ↑[f](𝛗n.t) ⊆ 𝛗f@❨n❩.t.
35 #f #t #n #p * #q #Hq #H0 destruct
36 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
37 /2 width=1 by in_comp_iref/
40 lemma lift_iref (f) (t) (n:pnat):
41 (𝛗f@❨n❩.t) ⇔ ↑[f](𝛗n.t).
42 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
45 lemma lift_iref_uni (t) (m) (n):
46 (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).