for X being set
for S being RealNormSpace
for f being PartFunc of REAL, the carrier of S holds
( f | X is Lipschitzian iff ex r being Real st
( 0 < r & ( for x1, x2 being Real st x1 in dom (f | X) & x2 in dom (f | X) holds
||.((f /. x1) - (f /. x2)).|| <= r * |.(x1 - x2).| ) ) )