let X be non empty set ; :: thesis: for Y, Z being non empty Subset of ExtREAL

for F being Function of X,Y

for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let Y, Z be non empty Subset of ExtREAL; :: thesis: for F being Function of X,Y

for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let F be Function of X,Y; :: thesis: for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let G be Function of X,Z; :: thesis: (inf F) + (inf G) <= inf (F + G)

A1: (inf (rng F)) + (inf (rng G)) <= inf ((rng F) + (rng G)) by Th8;

inf ((rng F) + (rng G)) <= inf (F + G) by Th15, XXREAL_2:60;

hence (inf F) + (inf G) <= inf (F + G) by A1, XXREAL_0:2; :: thesis: verum

for F being Function of X,Y

for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let Y, Z be non empty Subset of ExtREAL; :: thesis: for F being Function of X,Y

for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let F be Function of X,Y; :: thesis: for G being Function of X,Z holds (inf F) + (inf G) <= inf (F + G)

let G be Function of X,Z; :: thesis: (inf F) + (inf G) <= inf (F + G)

A1: (inf (rng F)) + (inf (rng G)) <= inf ((rng F) + (rng G)) by Th8;

inf ((rng F) + (rng G)) <= inf (F + G) by Th15, XXREAL_2:60;

hence (inf F) + (inf G) <= inf (F + G) by A1, XXREAL_0:2; :: thesis: verum