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14
15 include "delayed_updating/substitution/lift.ma".
16 include "delayed_updating/syntax/prototerm.ma".
17 include "ground/lib/subset_ext_equivalence.ma".
18
19 (* LIFT FOR PROTOTERM *******************************************************)
20
21 interpretation
22   "lift (prototerm)"
23   'UpArrow f t = (subset_ext_f1 ? ? (lift_gen ? proj_path f) t).
24
25 (* Basic constructions ******************************************************)
26
27 lemma in_comp_lift_bi (f) (p) (t):
28       p ϵ t → ↑[f]p ϵ ↑[f]t.
29 /2 width=1 by subset_in_ext_f1_dx/
30 qed.
31
32 lemma eq_lift_bi (f) (t1) (t2):
33       t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
34 /2 width=1 by subset_equivalence_ext_f1_bi/
35 qed.