let n be Element of NAT ; :: thesis: for X, X1 being set
for f being PartFunc of REAL,(REAL n) st f | X is Lipschitzian & X1 c= X holds
f | X1 is Lipschitzian
let X, X1 be set ; :: thesis: for f being PartFunc of REAL,(REAL n) st f | X is Lipschitzian & X1 c= X holds
f | X1 is Lipschitzian
let f be PartFunc of REAL,(REAL n); :: thesis: ( f | X is Lipschitzian & X1 c= X implies f | X1 is Lipschitzian )
assume that
A1: f | X is Lipschitzian and
A2: X1 c= X ; :: thesis: f | X1 is Lipschitzian
f | X1 = (f | X) | X1 by A2, RELAT_1:74;
hence f | X1 is Lipschitzian by A1; :: thesis: verum