Proposition: inverse relation

Let $⟨ X_{1}, \dots, X_{n - r} ⟩$ be a cinf-structure for the distribution $Z$ . Denote by $f_{k}$ a symmetrizing function of the vector field $X_{k}$ considered as a $C^{\infty}$ -symmetry of $S (X_{k})$ . Then

μ_{k} := \frac{1}{f_{k}} $ $ i s a n i n t e g r a t i n g f a c t o r f o r t h e $ k $ - t h P f a f f i a n e q u a t i o n r e f e r e n c e d i n t h e o r e m [[05 M Y R E S E A R C H / i n t e g r a t i o n b y P f a f f i a n e q u a t i o n s ∥ i n t e g r a t i o n b y P f a f f i a n e q u a t i o n s]] S p e c i a l c a s e : [[05 M Y R E S E A R C H / s y m m e t r i z i n g f a c t o r s i n t h e c a s e o f c o r a n k 1 ∥ s y m m e t r i z i n g f a c t o r s i n t h e c a s e o f c o r a n k 1]] .