let X be RealUnitarySpace; :: thesis: for seq being sequence of X holds (- 1) * seq = - seq
let seq be sequence of X; :: thesis: (- 1) * seq = - seq

now

let n be Element of NAT ; :: thesis: ((- 1) * seq) . n = (- seq) . n
thus ((- 1) * seq) . n = (- 1) * (seq . n) by NORMSP_1:def 8
.= - (seq . n) by RLVECT_1:29
.= (- seq) . n by Def10 ; :: thesis: verum

end;

hence (- 1) * seq = - seq by FUNCT_2:113; :: thesis: verum