let X be non empty set ; :: thesis: for f being PartFunc of X,REAL holds
( - (R_EAL f) = R_EAL ((- 1) (#) f) & - (R_EAL f) = R_EAL (- f) )
let f be PartFunc of X,REAL; :: thesis: ( - (R_EAL f) = R_EAL ((- 1) (#) f) & - (R_EAL f) = R_EAL (- f) )
- (R_EAL f) = (- 1) (#) (R_EAL f) by MESFUNC2:9;
hence ( - (R_EAL f) = R_EAL ((- 1) (#) f) & - (R_EAL f) = R_EAL (- f) ) by Th20; :: thesis: verum