import proveit
theory = proveit.Theory() # the theorem's theory
from proveit import defaults
from proveit.logic import InSet
from proveit.numbers import Complex
from proveit.physics.quantum.QPE import (_alpha_m_def, _Psi_ket_is_normalized_vec,
_t_in_natural_pos, _two_pow_t_is_nat_pos)
%proving _alpha_are_complex
defaults.assumptions = _alpha_are_complex.conditions
_alpha_m_def
alpha_m_defined = _alpha_m_def.instantiate()
_Psi_ket_is_normalized_vec
%qed