(* Basic_1: was: iso_trans *)
(* Basic_2A1: was: tsts_trans *)
-theorem theq_trans: ∀h,o. Transitive … (theq h o).
-#h #o #T1 #T * -T1 -T
-[ #s1 #s #d #Hs1 #Hs #X #H
- elim (theq_inv_sort1_deg … H … Hs) -s /2 width=3 by theq_sort/
+theorem theq_trans: Transitive … theq.
+#T1 #T * -T1 -T
+[ #s1 #s #X #H
+ elim (theq_inv_sort1 … H) -s /2 width=1 by theq_sort/
| #i1 #i #H <(theq_inv_lref1 … H) -H //
| #l1 #l #H <(theq_inv_gref1 … H) -H //
| #I #V1 #V #T1 #T #X #H
qed-.
(* Basic_2A1: was: tsts_canc_sn *)
-theorem theq_canc_sn: ∀h,o. left_cancellable … (theq h o).
+theorem theq_canc_sn: left_cancellable … theq.
/3 width=3 by theq_trans, theq_sym/ qed-.
(* Basic_2A1: was: tsts_canc_dx *)
-theorem theq_canc_dx: ∀h,o. right_cancellable … (theq h o).
+theorem theq_canc_dx: right_cancellable … theq.
/3 width=3 by theq_trans, theq_sym/ qed-.