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Theorem Dependencies

proveit.physics.quantum.QPE._phase_is_real

see proof

In [1]:
import proveit
# Automation is not needed when querying dependencies:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
from proveit.physics.quantum.QPE import _phase_is_real
In [2]:
%dependencies _phase_is_real

Unproven conjectures required (directly or indirectly) to prove _phase_is_real

proveit.numbers.number_sets.integers.nat_within_int
proveit.numbers.number_sets.rational_numbers.int_within_rational
proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
proveit.numbers.number_sets.real_numbers.rational_within_real
proveit.numbers.number_sets.real_numbers.zero_is_real

Axioms required (directly or indirectly) to prove _phase_is_real

proveit.logic.booleans.eq_true_elim
proveit.logic.booleans.eq_true_intro
proveit.logic.equality.equals_symmetry
proveit.logic.equality.equals_transitivity
proveit.logic.equality.substitution
proveit.logic.sets.inclusion.proper_subset_def
proveit.logic.sets.inclusion.subset_eq_def
proveit.numbers.number_sets.natural_numbers.successor_in_nats
proveit.numbers.number_sets.natural_numbers.zero_in_nats
proveit.numbers.numerals.decimals.one_def
proveit.physics.quantum.QPE._phase_in_interval

Theorems/conjectures that depend directly on _phase_is_real

proveit.physics.quantum.QPE._alpha_ideal_case
proveit.physics.quantum.QPE._alpha_m_evaluation
proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum
proveit.physics.quantum.QPE._best_floor_is_in_m_domain
proveit.physics.quantum.QPE._best_floor_is_int
proveit.physics.quantum.QPE._best_guarantee
proveit.physics.quantum.QPE._best_round_is_int
proveit.physics.quantum.QPE._delta_b_is_real
proveit.physics.quantum.QPE._phase_from_best_with_delta_b
proveit.physics.quantum.QPE._psi_t_formula
proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval