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15 include "static_2/syntax/tueq.ma".
17 (* TAIL SORT-IRRELEVANT EQUIVALENCE ON TERMS ********************************)
19 (* Main properties **********************************************************)
21 theorem tueq_trans: Transitive … tueq.
22 #T1 #T #H elim H -T1 -T
24 elim (tueq_inv_sort1 … H) -s /2 width=1 by tueq_sort/
27 | #p #I #V #T1 #T #_ #IHT #X #H
28 elim (tueq_inv_bind1 … H) -H /3 width=1 by tueq_bind/
29 | #V #T1 #T #_ #IHT #X #H
30 elim (tueq_inv_appl1 … H) -H /3 width=1 by tueq_appl/
31 | #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
32 elim (tueq_inv_cast1 … H) -H /3 width=1 by tueq_cast/
36 theorem tueq_canc_sn: left_cancellable … tueq.
37 /3 width=3 by tueq_trans, tueq_sym/ qed-.
39 theorem tueq_canc_dx: right_cancellable … tueq.
40 /3 width=3 by tueq_trans, tueq_sym/ qed-.
42 theorem tueq_repl: ∀T1,T2. T1 ≅ T2 →
43 ∀U1. T1 ≅ U1 → ∀U2. T2 ≅ U2 → U1 ≅ U2.
44 /3 width=3 by tueq_canc_sn, tueq_trans/ qed-.