-lemma teqx_dec: ∀T1,T2. Decidable (T1 ≛ T2).
-#T1 elim T1 -T1 [ * #s1 | #I1 #V1 #T1 #IHV #IHT ] * [1,3,5,7: * #s2 |*: #I2 #V2 #T2 ]
-[ /3 width=1 by teqx_sort, or_introl/
-|2,3,13:
- @or_intror #H
- elim (teqx_inv_sort1 … H) -H #x #H destruct
-|4,6,14:
- @or_intror #H
- lapply (teqx_inv_lref1 … H) -H #H destruct
-|5:
- elim (eq_nat_dec s1 s2) #Hs12 destruct /2 width=1 by or_introl/
- @or_intror #H
- lapply (teqx_inv_lref1 … H) -H #H destruct /2 width=1 by/
-|7,8,15:
- @or_intror #H
- lapply (teqx_inv_gref1 … H) -H #H destruct
-|9:
- elim (eq_nat_dec s1 s2) #Hs12 destruct /2 width=1 by or_introl/
- @or_intror #H
- lapply (teqx_inv_gref1 … H) -H #H destruct /2 width=1 by/
-|10,11,12:
- @or_intror #H
- elim (teqx_inv_pair1 … H) -H #X1 #X2 #_ #_ #H destruct
-|16:
- elim (eq_item2_dec I1 I2) #HI12 destruct
- [ elim (IHV V2) -IHV #HV12
- elim (IHT T2) -IHT #HT12
- [ /3 width=1 by teqx_pair, or_introl/ ]
- ]
- @or_intror #H
- elim (teqx_inv_pair … H) -H /2 width=1 by/
-]
-qed-.
+lemma teqx_dec:
+ ∀T1,T2. Decidable (T1 ≅ T2).
+/3 width=1 by teqg_dec, or_introl/ qed-.