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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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15 include "basic_2/static/lfeq_lfeq.ma".
16 include "basic_2/static/ffeq.ma".
18 (* EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *****************************)
20 (* Main properties **********************************************************)
22 theorem ffeq_trans: tri_transitive … ffeq.
23 #G1 #G #L1 #L #T1 #T * -G -L -T
24 #L #HL1 #G2 #L2 #T2 * -G2 -L2 -T2 /3 width=3 by fleq_intro, lfeq_trans/
27 theorem ffeq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2.
28 ⦃G, L, T⦄ ≡ ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≡ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄.
29 /3 width=5 by ffeq_trans, ffeq_sym/ qed-.
31 theorem ffeq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T.
32 ⦃G1, L1, T1⦄ ≡ ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≡ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄.
33 /3 width=5 by ffeq_trans, ffeq_sym/ qed-.