let X be non empty set ; :: thesis: for S being SigmaField of X

for f being PartFunc of X,ExtREAL st f is_simple_func_in S holds

- f is_simple_func_in S

let S be SigmaField of X; :: thesis: for f being PartFunc of X,ExtREAL st f is_simple_func_in S holds

- f is_simple_func_in S

let f be PartFunc of X,ExtREAL; :: thesis: ( f is_simple_func_in S implies - f is_simple_func_in S )

assume A1: f is_simple_func_in S ; :: thesis: - f is_simple_func_in S

- f = (- 1) (#) f by MESFUNC2:9;

hence - f is_simple_func_in S by A1, MESFUNC5:39; :: thesis: verum

for f being PartFunc of X,ExtREAL st f is_simple_func_in S holds

- f is_simple_func_in S

let S be SigmaField of X; :: thesis: for f being PartFunc of X,ExtREAL st f is_simple_func_in S holds

- f is_simple_func_in S

let f be PartFunc of X,ExtREAL; :: thesis: ( f is_simple_func_in S implies - f is_simple_func_in S )

assume A1: f is_simple_func_in S ; :: thesis: - f is_simple_func_in S

- f = (- 1) (#) f by MESFUNC2:9;

hence - f is_simple_func_in S by A1, MESFUNC5:39; :: thesis: verum