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