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3 (*      ||M||                                                             *)
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14
15 include "static_2/static/feqg_feqg.ma".
16 include "static_2/static/feqx.ma".
17
18 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
19
20 (* Advanced properties ******************************************************)
21
22 lemma feqx_dec (G1) (G2) (L1) (L2) (T1) (T2):
23       Decidable (❨G1,L1,T1❩ ≅ ❨G2,L2,T2❩).
24 /3 width=1 by feqg_dec, sfull_dec/ qed-.
25 (*
26 lemma feqx_sym: tri_symmetric … feqx.
27 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
28 /3 width=1 by feqx_intro_dx, reqx_sym, teqx_sym/
29 qed-.
30
31 (* Main properties **********************************************************)
32
33 theorem feqx_trans: tri_transitive … feqx.
34 #G1 #G #L1 #L #T1 #T * -G -L -T
35 #L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
36 /4 width=5 by feqx_intro_sn, reqx_trans, teqx_reqx_div, teqx_trans/
37 qed-.
38
39 theorem feqx_canc_sn: ∀G,G1,L,L1,T,T1. ❨G,L,T❩ ≛ ❨G1,L1,T1❩→
40                       ∀G2,L2,T2. ❨G,L,T❩ ≛ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩.
41 /3 width=5 by feqx_trans, feqx_sym/ qed-.
42
43 theorem feqx_canc_dx: ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≛ ❨G,L,T❩ →
44                       ∀G2,L2,T2. ❨G2,L2,T2❩ ≛ ❨G,L,T❩ → ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩.
45 /3 width=5 by feqx_trans, feqx_sym/ qed-.
46
47 (* Main inversion lemmas with degree-based equivalence on terms *************)
48
49 theorem feqx_tneqx_repl_dx: ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩ →
50                             ∀U1,U2. ❨G1,L1,U1❩ ≛ ❨G2,L2,U2❩ →
51                             (T2 ≛ U2 → ⊥) → (T1 ≛ U1 → ⊥).
52 #G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
53 elim (feqx_inv_gen_sn … HT) -HT #_ #_ #HT
54 elim (feqx_inv_gen_sn … HU) -HU #_ #_ #HU
55 /3 width=5 by teqx_repl/
56 qed-.
57 *)