logo

Theorem Dependencies

proveit.physics.quantum.QPE._two_pow_t_is_nat_pos

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 _two_pow_t_is_nat_pos
In [2]:
%dependencies _two_pow_t_is_nat_pos

Unproven conjectures required (directly or indirectly) to prove _two_pow_t_is_nat_pos

proveit.numbers.exponentiation.exp_natpos_closure
proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
proveit.numbers.numerals.decimals.add_1_1

Axioms required (directly or indirectly) to prove _two_pow_t_is_nat_pos

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._t_in_natural_pos

Theorems/conjectures that depend directly on _two_pow_t_is_nat_pos

proveit.physics.quantum.QPE._alpha_are_complex
proveit.physics.quantum.QPE._alpha_ideal_case
proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum
proveit.physics.quantum.QPE._alpha_m_mod_evaluation
proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
proveit.physics.quantum.QPE._alpha_summed
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_guarantee_delta_nonzero
proveit.physics.quantum.QPE._best_round_is_int
proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
proveit.physics.quantum.QPE._delta_b_in_interval
proveit.physics.quantum.QPE._delta_b_is_real
proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
proveit.physics.quantum.QPE._failure_upper_bound_lemma
proveit.physics.quantum.QPE._mod_add_closure
proveit.physics.quantum.QPE._modabs_in_full_domain_simp
proveit.physics.quantum.QPE._non_int_delta_b_diff
proveit.physics.quantum.QPE._phase_from_best_with_delta_b
proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
proveit.physics.quantum.QPE._success_complements_failure
proveit.physics.quantum.QPE.qpe_best_guarantee