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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "static_2/static/rdeq_rdeq.ma".
16 include "static_2/static/fdeq.ma".
18 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
20 (* Advanced properties ******************************************************)
22 lemma fdeq_sym: tri_symmetric … fdeq.
23 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
24 /3 width=1 by fdeq_intro_dx, rdeq_sym, tdeq_sym/
27 (* Main properties **********************************************************)
29 theorem fdeq_trans: tri_transitive … fdeq.
30 #G1 #G #L1 #L #T1 #T * -G -L -T
31 #L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
32 /4 width=5 by fdeq_intro_sn, rdeq_trans, tdeq_rdeq_div, tdeq_trans/
35 theorem fdeq_canc_sn: ∀G,G1,L,L1,T,T1. ⦃G, L, T⦄ ≛ ⦃G1, L1, T1⦄→
36 ∀G2,L2,T2. ⦃G, L, T⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄.
37 /3 width=5 by fdeq_trans, fdeq_sym/ qed-.
39 theorem fdeq_canc_dx: ∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≛ ⦃G, L, T⦄ →
40 ∀G2,L2,T2. ⦃G2, L2, T2⦄ ≛ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄.
41 /3 width=5 by fdeq_trans, fdeq_sym/ qed-.
43 (* Main inversion lemmas with degree-based equivalence on terms *************)
45 theorem fdeq_tdneq_repl_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄ →
46 ∀U1,U2. ⦃G1, L1, U1⦄ ≛ ⦃G2, L2, U2⦄ →
47 (T2 ≛ U2 → ⊥) → (T1 ≛ U1 → ⊥).
48 #G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
49 elim (fdeq_inv_gen_sn … HT) -HT #_ #_ #HT
50 elim (fdeq_inv_gen_sn … HU) -HU #_ #_ #HU
51 /3 width=5 by tdeq_repl/