+++ /dev/null
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-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/syntax/tdeq.ma".
-
-(* DEGREE-BASED EQUIVALENCE ON TERMS ****************************************)
-
-(* Main properties **********************************************************)
-
-theorem tdeq_trans: ∀h,o. Transitive … (tdeq h o).
-#h #o #T1 #T #H elim H -T1 -T
-[ #s1 #s #d #Hs1 #Hs #X #H
- elim (tdeq_inv_sort1_deg … H … Hs) -s /2 width=3 by tdeq_sort/
-| #i1 #i #H <(tdeq_inv_lref1 … H) -H //
-| #l1 #l #H <(tdeq_inv_gref1 … H) -H //
-| #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
- elim (tdeq_inv_pair1 … H) -H /3 width=1 by tdeq_pair/
-]
-qed-.
-
-theorem tdeq_canc_sn: ∀h,o. left_cancellable … (tdeq h o).
-/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
-
-theorem tdeq_canc_dx: ∀h,o. right_cancellable … (tdeq h o).
-/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
-
-theorem tdeq_repl: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
- ∀U1. T1 ≛[h, o] U1 → ∀U2. T2 ≛[h, o] U2 → U1 ≛[h, o] U2.
-/3 width=3 by tdeq_canc_sn, tdeq_trans/ qed-.
-
-(* Negated main properies ***************************************************)
-
-theorem tdeq_tdneq_trans: ∀h,o,T1,T. T1 ≛[h, o] T → ∀T2. (T ≛[h, o] T2 → ⊥) →
- T1 ≛[h, o] T2 → ⊥.
-/3 width=3 by tdeq_canc_sn/ qed-.
-
-theorem tdneq_tdeq_canc_dx: ∀h,o,T1,T. (T1 ≛[h, o] T → ⊥) → ∀T2. T2 ≛[h, o] T →
- T1 ≛[h, o] T2 → ⊥.
-/3 width=3 by tdeq_trans/ qed-.