let f be PartFunc of REAL, the carrier of S; :: thesis: ( f is empty implies f is Lipschitzian )
assume A1: f is empty ; :: thesis: f is Lipschitzian
take 1 ; :: according to NFCONT_3:def 3 :: thesis: ( 0 < 1 & ( for x1, x2 being real number st x1 in dom f & x2 in dom f holds
||.((f /. x1) - (f /. x2)).|| <= 1 * (abs (x1 - x2)) ) )
thus ( 0 < 1 & ( for x1, x2 being real number st x1 in dom f & x2 in dom f holds
||.((f /. x1) - (f /. x2)).|| <= 1 * (abs (x1 - x2)) ) ) by A1; :: thesis: verum