Orthonormal basis

Set

context $V$…pre-Hilbert space
definiendum $B\in \mathrm{OrthonormalBasis}(V)$
context $B\in \mathrm{Basis}(V)$
$v,w\in B$
postulate $v\ne w\implies \langle v|w\rangle = 0 $
postulate $\Vert v\Vert = 1 $

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