let u, v be VECTOR of ((0). V0); :: thesis: for a being Complex holds nilfunc . [(a * u),v] = a * (nilfunc . [u,v])
let a be Complex; :: thesis: nilfunc . [(a * u),v] = a * (nilfunc . [u,v])
( u = 0. V0 & v = 0. V0 )
by Lm1, TARSKI:def 1;
hence
nilfunc . [(a * u),v] = a * (nilfunc . [u,v])
by Lm1, Lm3, TARSKI:def 1; :: thesis: verum