let X be RealUnitarySpace; :: thesis: for seq being sequence of X st seq is convergent holds
lim (- seq) = - (lim seq)
let seq be sequence of X; :: thesis: ( seq is convergent implies lim (- seq) = - (lim seq) )
assume seq is convergent ; :: thesis: lim (- seq) = - (lim seq)
then lim ((- 1) * seq) = (- 1) * (lim seq) by Th15;
then lim (- seq) = (- 1) * (lim seq) by BHSP_1:55;
hence lim (- seq) = - (lim seq) by RLVECT_1:16; :: thesis: verum