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Theorem Dependencies

proveit.physics.quantum.QPE._best_floor_is_in_m_domain

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 _best_floor_is_in_m_domain
In [2]:
%dependencies _best_floor_is_in_m_domain

Unproven conjectures required (directly or indirectly) to prove _best_floor_is_in_m_domain

proveit.numbers.addition.add_int_closure_bin
proveit.numbers.exponentiation.exp_natpos_closure
proveit.numbers.multiplication.elim_one_right
proveit.numbers.multiplication.mult_real_closure_bin
proveit.numbers.multiplication.mult_zero_right
proveit.numbers.multiplication.strong_bound_via_right_factor_bound
proveit.numbers.multiplication.weak_bound_via_right_factor_bound
proveit.numbers.negation.int_closure
proveit.numbers.number_sets.complex_numbers.real_within_complex
proveit.numbers.number_sets.integers.in_interval
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_is_pos
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.interval_co_lower_bound
proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
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.ordering.relax_less
proveit.numbers.rounding.floor_increasing_less_eq
proveit.numbers.rounding.floor_of_integer
proveit.numbers.rounding.floor_of_real_below_int

Axioms required (directly or indirectly) to prove _best_floor_is_in_m_domain

proveit.logic.booleans.conjunction.and_t_t
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.numbers.rounding.floor_is_an_int
proveit.physics.quantum.QPE._phase_in_interval
proveit.physics.quantum.QPE._t_in_natural_pos

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

proveit.physics.quantum.QPE._best_floor_def

Theorems/conjectures that depend directly on _best_floor_is_in_m_domain

proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval