Theorem Dependencies¶

proveit.numbers.number_sets.integers.zero_is_int ¶

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.integers import zero_is_int

In [2]:

%dependencies zero_is_int

Unproven conjectures required (directly or indirectly) to prove zero_is_int

proveit.numbers.number_sets.integers.nat_within_int

Axioms required (directly or indirectly) to prove zero_is_int

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.zero_in_nats

Theorems/conjectures that depend directly on zero_is_int

proveit.numbers.divisibility.non_zero_divides_zero

proveit.numbers.summation.finite_geom_sum

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_summed

proveit.physics.quantum.QPE._best_floor_is_in_m_domain

proveit.physics.quantum.QPE._best_guarantee

proveit.physics.quantum.QPE._best_guarantee_delta_nonzero

proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int

proveit.physics.quantum.QPE._failure_upper_bound

proveit.physics.quantum.QPE._failure_upper_bound_lemma

proveit.physics.quantum.QPE._non_int_delta_b_diff

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._psi_t_output

proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval

proveit.physics.quantum.QPE._scaled_delta_b_is_zero_or_non_int

proveit.physics.quantum.QPE._success_complements_failure

proveit.physics.quantum.QPE.qpe_exact