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14
15 include "delayed_updating/syntax/prototerm.ma".
16 include "ground/lib/subset_equivalence.ma".
17
18 (* EQUIVALENCE FOR PROTOTERM ************************************************)
19
20 (* Constructions with prototerm_grafted *************************************)
21
22 lemma grafted_empty_dx (t):
23       t ⇔ t⋔𝐞.
24 /2 width=1 by conj/
25 qed.
26
27 (* Constructions with prototerm_root ****************************************)
28
29 lemma prototerm_root_incl_repl:
30       ∀t1,t2. t1 ⊆ t2 → ▵t1 ⊆ ▵t2.
31 #t1 #t2 #Ht #p * #q #Hq
32 /3 width=2 by ex_intro/
33 qed.
34
35 lemma prototerm_root_eq_repl:
36       ∀t1,t2. t1 ⇔ t2 → ▵t1 ⇔ ▵t2.
37 #t1 #t2 * #H1 #H2
38 /3 width=3 by conj, prototerm_root_incl_repl/
39 qed.