let V be RealLinearSpace; :: thesis: for u, v, w, y being VECTOR of V st u,v are_Ort_wrt w,y holds
v,u are_Ort_wrt w,y
let u, v, w, y be VECTOR of V; :: thesis: ( u,v are_Ort_wrt w,y implies v,u are_Ort_wrt w,y )
assume u,v are_Ort_wrt w,y ; :: thesis: v,u are_Ort_wrt w,y
then ex a1, a2, b1, b2 being Real st
( u = (a1 * w) + (a2 * y) & v = (b1 * w) + (b2 * y) & (a1 * b1) + (a2 * b2) = 0 ) by Def2;
hence v,u are_Ort_wrt w,y by Def2; :: thesis: verum