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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_2A/multiple/lleq_lleq.ma".
16 include "basic_2A/multiple/fleq.ma".
18 (* LAZY EQUIVALENCE FOR CLOSURES *******************************************)
20 (* Main properties **********************************************************)
22 theorem fleq_trans: ∀l. tri_transitive … (fleq l).
23 #l #G1 #G #L1 #L #T1 #T * -G -L -T
24 #L #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
25 /3 width=3 by lleq_trans, fleq_intro/
28 theorem fleq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2,l.
29 ⦃G, L, T⦄ ≡[l] ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≡[l] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
30 /3 width=5 by fleq_trans, fleq_sym/ qed-.
32 theorem fleq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T,l.
33 ⦃G1, L1, T1⦄ ≡[l] ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≡[l] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
34 /3 width=5 by fleq_trans, fleq_sym/ qed-.