let Y be set ; :: thesis: for C being non empty set

for f being PartFunc of C,REAL st f | Y is constant holds

(- f) | Y is constant

let C be non empty set ; :: thesis: for f being PartFunc of C,REAL st f | Y is constant holds

(- f) | Y is constant

let f be PartFunc of C,REAL; :: thesis: ( f | Y is constant implies (- f) | Y is constant )

(- f) | Y = - (f | Y) by Th46;

hence ( f | Y is constant implies (- f) | Y is constant ) ; :: thesis: verum

for f being PartFunc of C,REAL st f | Y is constant holds

(- f) | Y is constant

let C be non empty set ; :: thesis: for f being PartFunc of C,REAL st f | Y is constant holds

(- f) | Y is constant

let f be PartFunc of C,REAL; :: thesis: ( f | Y is constant implies (- f) | Y is constant )

(- f) | Y = - (f | Y) by Th46;

hence ( f | Y is constant implies (- f) | Y is constant ) ; :: thesis: verum