+definition lfxs_confluent: relation … ≝
+ λR1,R2.
+ ∀K1,K,V1. K1 ⪤*[R1, V1] K → ∀V. R1 K1 V1 V →
+ ∀K2. K ⪤*[R2, V] K2 → K ⪤*[R2, V1] K2.
+
+definition lfxs_transitive: relation3 ? (relation3 ?? term) ? ≝
+ λR1,R2,R3.
+ ∀K1,K,V1. K1 ⪤*[R1, V1] K →
+ ∀V. R1 K1 V1 V → ∀V2. R2 K V V2 → R3 K1 V1 V2.
+