+definition LTC: ∀A:Type[0]. ∀B. (A→relation B) → (A→relation B) ≝
+ λA,B,R,a. TC … (R a).
+
+definition s_r_trans: ∀A,B. relation2 (A→relation B) (relation A) ≝ λA,B,R1,R2.
+ ∀L2,T1,T2. R1 L2 T1 T2 → ∀L1. R2 L1 L2 → LTC … R1 L1 T1 T2.
+
+definition s_rs_trans: ∀A,B. relation2 (A→relation B) (relation A) ≝ λA,B,R1,R2.
+ ∀L2,T1,T2. LTC … R1 L2 T1 T2 → ∀L1. R2 L1 L2 → LTC … R1 L1 T1 T2.
+