let V be RealLinearSpace; :: thesis: for u, u1, v, w, y being VECTOR of V st Gen w,y holds
u,v,u1,u1 are_Ort_wrt w,y
let u, u1, v, w, y be VECTOR of V; :: thesis: ( Gen w,y implies u,v,u1,u1 are_Ort_wrt w,y )
A1: u1 - u1 = 0. V by RLVECT_1:15;
assume Gen w,y ; :: thesis: u,v,u1,u1 are_Ort_wrt w,y
then v - u,u1 - u1 are_Ort_wrt w,y by A1, ANALMETR:5;
hence u,v,u1,u1 are_Ort_wrt w,y by ANALMETR:def 3; :: thesis: verum