Theorem Dependencies¶

proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero ¶

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.numbers.number_sets.real_numbers import rational_nonzero_within_real_nonzero

In [2]:

%dependencies rational_nonzero_within_real_nonzero

Unproven conjectures required (directly or indirectly) to prove rational_nonzero_within_real_nonzero

proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero

Theorems/conjectures that depend directly on rational_nonzero_within_real_nonzero

proveit.numbers.exponentiation.sqrt2_is_not_rational

proveit.numbers.summation.finite_geom_sum

proveit.numbers.summation.sum_first_n_int

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._alpha_m_mod_evaluation

proveit.physics.quantum.QPE._alpha_sqrd_upper_bound

proveit.physics.quantum.QPE._alpha_summed

proveit.physics.quantum.QPE._best_guarantee

proveit.physics.quantum.QPE._best_guarantee_delta_nonzero

proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval

proveit.physics.quantum.QPE._delta_b_in_interval

proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt

proveit.physics.quantum.QPE._fail_sum

proveit.physics.quantum.QPE._fail_sum_prob_conds_equiv_lemma

proveit.physics.quantum.QPE._failure_upper_bound

proveit.physics.quantum.QPE._failure_upper_bound_lemma

proveit.physics.quantum.QPE._modabs_in_full_domain_simp

proveit.physics.quantum.QPE._non_int_delta_b_diff

proveit.physics.quantum.QPE._precision_guarantee

proveit.physics.quantum.QPE._precision_guarantee_lemma_01

proveit.physics.quantum.QPE._precision_guarantee_lemma_02

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

proveit.physics.quantum.QPE.qpe_exact