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14
15 include "static_2/syntax/teqg_teqg.ma".
16 include "static_2/syntax/teqx.ma".
17
18 (* SORT-IRRELEVANT EQUIVALENCE ON TERMS *************************************)
19
20 (* Main properties **********************************************************)
21
22 theorem teqx_trans:
23         Transitive … teqx.
24 /2 width=3 by teqg_trans/ qed-.
25
26 theorem teqx_canc_sn:
27         left_cancellable … teqx.
28 /2 width=3 by teqg_canc_sn/ qed-.
29
30 theorem teqx_canc_dx:
31         right_cancellable … teqx.
32 /2 width=3 by teqg_canc_dx/ qed-.
33 (*
34 theorem teqx_repl: ∀T1,T2. T1 ≛ T2 →
35                    ∀U1. T1 ≛ U1 → ∀U2. T2 ≛ U2 → U1 ≛ U2.
36 /3 width=3 by teqx_canc_sn, teqx_trans/ qed-.
37
38 (* Negated main properies ***************************************************)
39
40 theorem teqx_tneqx_trans: ∀T1,T. T1 ≛ T → ∀T2. (T ≛ T2 → ⊥) → T1 ≛ T2 → ⊥.
41 /3 width=3 by teqx_canc_sn/ qed-.
42
43 theorem tneqx_teqx_canc_dx: ∀T1,T. (T1 ≛ T → ⊥) → ∀T2. T2 ≛ T → T1 ≛ T2 → ⊥.
44 /3 width=3 by teqx_trans/ qed-.
45 *)