@(TC_ind_dx … P ? H … Ha12) /3 width=4/
qed-.
-definition Conf3: ∀A,B. relation2 A B → relation A → Prop ≝ λA,B,S,R.
- ∀b,a1. S a1 b → ∀a2. R a1 a2 → S a2 b.
-
lemma TC_Conf3: ∀A,B,S,R. Conf3 A B S R → Conf3 A B S (TC … R).
#A #B #S #R #HSR #b #a1 #Ha1 #a2 #H elim H -a2 /2 width=3/
qed.