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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/syntax/tdeq.ma".
17 (* DEGREE-BASED EQUIVALENCE ON TERMS ****************************************)
19 (* Main properties **********************************************************)
21 theorem tdeq_trans: ∀h,o. Transitive … (tdeq h o).
22 #h #o #T1 #T #H elim H -T1 -T
23 [ #s1 #s #d #Hs1 #Hs #X #H
24 elim (tdeq_inv_sort1_deg … H … Hs) -s /2 width=3 by tdeq_sort/
25 | #i1 #i #H <(tdeq_inv_lref1 … H) -H //
26 | #l1 #l #H <(tdeq_inv_gref1 … H) -H //
27 | #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H destruct
28 elim (tdeq_inv_pair1 … H) -H /3 width=1 by tdeq_pair/