let n be Element of NAT ; :: thesis: for X being set
for p being Real
for f being PartFunc of REAL,(REAL n) st f | X is Lipschitzian & X c= dom f holds
(p (#) f) | X is Lipschitzian
let X be set ; :: thesis: for p being Real
for f being PartFunc of REAL,(REAL n) st f | X is Lipschitzian & X c= dom f holds
(p (#) f) | X is Lipschitzian
let p be Real; :: thesis: for f being PartFunc of REAL,(REAL n) st f | X is Lipschitzian & X c= dom f holds
(p (#) f) | X is Lipschitzian
let f be PartFunc of REAL,(REAL n); :: thesis: ( f | X is Lipschitzian & X c= dom f implies (p (#) f) | X is Lipschitzian )
assume A1: ( f | X is Lipschitzian & X c= dom f ) ; :: thesis: (p (#) f) | X is Lipschitzian
reconsider g = f as PartFunc of REAL,(REAL-NS n) by REAL_NS1:def 4;
A2: (p (#) g) | X is Lipschitzian by A1, NFCONT_3:30;
p (#) g = p (#) f by Th6;
hence (p (#) f) | X is Lipschitzian by A2; :: thesis: verum