Theorem Dependencies¶

proveit.physics.quantum.QPE._delta_b_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 _delta_b_is_real

In [2]:

%dependencies _delta_b_is_real

Unproven conjectures required (directly or indirectly) to prove _delta_b_is_real

proveit.numbers.addition.add_real_closure_bin

proveit.numbers.division.div_real_closure

proveit.numbers.exponentiation.exp_natpos_closure

proveit.numbers.negation.real_closure

proveit.numbers.number_sets.integers.nat_pos_within_int

proveit.numbers.number_sets.integers.nat_within_int

proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat

proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound

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

proveit.numbers.numerals.decimals.add_1_1

proveit.numbers.numerals.decimals.less_0_1

proveit.numbers.ordering.less_is_not_eq_nat

Axioms required (directly or indirectly) to prove _delta_b_is_real

proveit.logic.booleans.bools_def

proveit.logic.booleans.disjunction.left_in_bool

proveit.logic.booleans.disjunction.or_f_f

proveit.logic.booleans.disjunction.or_t_f

proveit.logic.booleans.disjunction.right_in_bool

proveit.logic.booleans.eq_true_elim

proveit.logic.booleans.eq_true_intro

proveit.logic.booleans.false_not_true

proveit.logic.booleans.implication.affirmation_via_contradiction

proveit.logic.booleans.implication.denial_via_contradiction

proveit.logic.booleans.negation.negation_elim

proveit.logic.booleans.negation.not_f

proveit.logic.booleans.negation.not_t

proveit.logic.equality.equality_in_bool

proveit.logic.equality.equals_reflexivity

proveit.logic.equality.equals_symmetry

proveit.logic.equality.equals_transitivity

proveit.logic.equality.not_equals_def

proveit.logic.equality.substitution

proveit.logic.sets.enumeration.enum_set_def

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.numbers.ordering.less_eq_def

proveit.numbers.ordering.transitivity_less_less

proveit.physics.quantum.QPE._phase_in_interval

proveit.physics.quantum.QPE._t_in_natural_pos

Conservative definitions used (but not logically required) to prove _delta_b_is_real

proveit.numbers.numerals.decimals.tuple_len_2_typical_eq

proveit.physics.quantum.QPE._delta_b_def

Theorems/conjectures that depend directly on _delta_b_is_real

proveit.physics.quantum.QPE._alpha_sqrd_upper_bound

proveit.physics.quantum.QPE._alpha_summed

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._failure_upper_bound

proveit.physics.quantum.QPE._failure_upper_bound_lemma