|a|/(1+|a|)+|b|/(1+|b|)>=|a+b|/(1+|a+b|)|a|/(1+|a|)+|b|/(1+|b|)>=|a|/(1+|a|+|b|)+|b|/(1+|b|+|a|)=(|a|+|b|)/(1+|a|+|b|)=1-1/(1+|a|+|b|)>=1-1/(1+|a+b|)=|a+b|/(1+|a+b|) (|a|+|b|/>=|a+b|)