let V be RealLinearSpace; :: thesis: for y, w being VECTOR of
for a, b being Element of ex p being Element of st p # a = b
let y, w be VECTOR of ; :: thesis: for a, b being Element of ex p being Element of st p # a = b
let a, b be Element of ; :: thesis: ex p being Element of st p # a = b
reconsider u = a, v = b as VECTOR of ;
consider u1 being VECTOR of such that
A1: u # u1 = v by Th7;
reconsider p = u1 as Element of ;
p # a = u # u1 by Def8;
hence ex p being Element of st p # a = b by A1; :: thesis: verum