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It suffices to declare (X_1, X_2, X_3, X_4) as a vector frame on the manifold and to pass it as argument of display:

XF = N.vector_frame(('X_1', 'X_2', 'X_3', 'X_4'), (X_1, X_2, X_3, X_4),
                     symbol_dual=('X^1', 'X^2', 'X^3', 'X^4'))
vw = X_2.bracket(X_4)
vw.display(XF)

yields

X_1

Type N.vector_frame? for more details; see also vector_frame online documentation.

Remark: if you construct the manifold N with the argument start_index=1, i.e.

N = Manifold(4, 'N', start_index=1)

the call to vector_frame can be much abridged:

XF = N.vector_frame('X', (X_1, X_2, X_3, X_4))