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

for M being sigma_Measure of S

for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let S be SigmaField of X; :: thesis: for M being sigma_Measure of S

for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let M be sigma_Measure of S; :: thesis: for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let T be N_Sub_set_fam of X; :: thesis: ( ( for A being set st A in T holds

A in S ) implies ( union T in S & meet T in S ) )

assume A1: for A being set st A in T holds

A in S ; :: thesis: ( union T in S & meet T in S )

T c= S by A1;

hence ( union T in S & meet T in S ) by Def5, Th22; :: thesis: verum

for M being sigma_Measure of S

for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let S be SigmaField of X; :: thesis: for M being sigma_Measure of S

for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let M be sigma_Measure of S; :: thesis: for T being N_Sub_set_fam of X st ( for A being set st A in T holds

A in S ) holds

( union T in S & meet T in S )

let T be N_Sub_set_fam of X; :: thesis: ( ( for A being set st A in T holds

A in S ) implies ( union T in S & meet T in S ) )

assume A1: for A being set st A in T holds

A in S ; :: thesis: ( union T in S & meet T in S )

T c= S by A1;

hence ( union T in S & meet T in S ) by Def5, Th22; :: thesis: verum