This paper presents a sketch of a formal proof of strong equivalence, where both grammars generate equivalent parse results, between any LTAG (Lexicalized Tree Adjoining Grammar: Schabes, Abeille and Joshi (1988)) G and an HPSG (Head-Driven Phrase Structure Grammar: Pollard and Sag (1994))-style grammar converted from G by a grammar conversion (Yoshinaga and Miyao, 2001). Our proof theoretically justifies some applications of the grammar conversion that exploit the nature of strong equivalence (Yoshinaga et al., 2001b; Yoshinaga et al., 2001a), applications which contribute much to the developments of the two formalisms