def prove(Eq):
n = Symbol.n(domain=[2, oo], integer=True)
W = Symbol.W(shape=(n, n), complex=True)
Eq << apply(W)
U = Symbol.U(definition=Eq[0].lhs)
V = Symbol.V(definition=Eq[0].rhs)
Eq << U.this.definition
Eq << V.this.definition
i = Symbol.i(integer=True, domain=[0, n])
j = Symbol.j(integer=True, domain=[0, n])
Eq << (V[i, j].this.definition, U[i, j].this.definition)
Eq << (Eq[-1].this.rhs.as_KroneckerDelta(),
Eq[-2].this.rhs.as_KroneckerDelta())
Eq << Eq[-2] - Eq[-1]
Eq << Eq[-1].reference((j, ), (i, ))
Eq << Eq[-1].subs(Eq[1]).subs(Eq[2])
Eq << Eq[-1].forall((j, ), (i, ))
def prove(Eq):
n = Symbol.n(domain=[2, oo], integer=True)
Eq << apply(n)
U = Symbol.U(definition=Eq[0].lhs)
V = Symbol.V(definition=Eq[0].rhs)
Eq << U.this.definition
Eq << V.this.definition
i = Symbol.i(integer=True, domain=[0, n])
Eq << Eq[-1][i]
Eq << U[i].this.definition
Eq << Eq[-2].this.rhs.as_KroneckerDelta()
Eq << Eq[-2] - Eq[-1]
Eq << Eq[-1].reference((i, ))
Eq << Eq[-1].subs(Eq[1]).subs(Eq[2])
