(* *)
(**************************************************************************)
+include "static_2/syntax/teqg_teqg.ma".
include "static_2/syntax/teqx.ma".
(* SORT-IRRELEVANT EQUIVALENCE ON TERMS *************************************)
(* Main properties **********************************************************)
-theorem teqx_trans: Transitive … teqx.
-#T1 #T #H elim H -T1 -T
-[ #s1 #s #X #H
- elim (teqx_inv_sort1 … H) -s /2 width=1 by teqx_sort/
-| #i1 #i #H <(teqx_inv_lref1 … H) -H //
-| #l1 #l #H <(teqx_inv_gref1 … H) -H //
-| #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
- elim (teqx_inv_pair1 … H) -H /3 width=1 by teqx_pair/
-]
-qed-.
+theorem teqx_trans:
+ Transitive … teqx.
+/2 width=3 by teqg_trans/ qed-.
-theorem teqx_canc_sn: left_cancellable … teqx.
-/3 width=3 by teqx_trans, teqx_sym/ qed-.
-
-theorem teqx_canc_dx: right_cancellable … teqx.
-/3 width=3 by teqx_trans, teqx_sym/ qed-.
+theorem teqx_canc_sn:
+ left_cancellable … teqx.
+/2 width=3 by teqg_canc_sn/ qed-.
+theorem teqx_canc_dx:
+ right_cancellable … teqx.
+/2 width=3 by teqg_canc_dx/ qed-.
+(*
theorem teqx_repl: ∀T1,T2. T1 ≛ T2 →
∀U1. T1 ≛ U1 → ∀U2. T2 ≛ U2 → U1 ≛ U2.
/3 width=3 by teqx_canc_sn, teqx_trans/ qed-.
theorem tneqx_teqx_canc_dx: ∀T1,T. (T1 ≛ T → ⊥) → ∀T2. T2 ≛ T → T1 ≛ T2 → ⊥.
/3 width=3 by teqx_trans/ qed-.
+*)