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Theorem Dependencies

proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval

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 _scaled_delta_b_floor_in_interval
In [2]:
%dependencies _scaled_delta_b_floor_in_interval

Unproven conjectures required (directly or indirectly) to prove _scaled_delta_b_floor_in_interval

proveit.core_expr_types.tuples.tuple_len_0_typical_eq
proveit.logic.equality.four_chain_transitivity
proveit.numbers.addition.add_int_closure_bin
proveit.numbers.addition.add_real_closure_bin
proveit.numbers.addition.subtraction.nonneg_difference
proveit.numbers.division.div_complex_closure
proveit.numbers.division.frac_one_denom
proveit.numbers.division.mult_frac_cancel_numer_left
proveit.numbers.exponentiation.exp_int_closure
proveit.numbers.exponentiation.exp_natpos_closure
proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
proveit.numbers.multiplication.commutation
proveit.numbers.multiplication.distribute_through_subtract
proveit.numbers.multiplication.elim_one_left
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.negation.real_closure
proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
proveit.numbers.number_sets.complex_numbers.real_within_complex
proveit.numbers.number_sets.integers.in_interval
proveit.numbers.number_sets.integers.int_interval_within_int
proveit.numbers.number_sets.integers.nat_pos_within_int
proveit.numbers.number_sets.integers.nat_pos_within_nonzero_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.rational_numbers.nonzero_int_within_rational_nonzero
proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
proveit.numbers.number_sets.real_numbers.in_IntervalCO
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_nonzero_within_real_nonzero
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.posnat1
proveit.numbers.numerals.decimals.posnat2
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
proveit.numbers.rounding.real_minus_floor_upper_bound

Axioms required (directly or indirectly) to prove _scaled_delta_b_floor_in_interval

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.numbers.rounding.floor_of_x_less_eq_x
proveit.physics.quantum.QPE._phase_in_interval
proveit.physics.quantum.QPE._t_in_natural_pos

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

proveit.physics.quantum.QPE._best_floor_def
proveit.physics.quantum.QPE._delta_b_def

Theorems/conjectures that depend directly on _scaled_delta_b_floor_in_interval

proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
proveit.physics.quantum.QPE._delta_b_in_interval
proveit.physics.quantum.QPE._failure_upper_bound
proveit.physics.quantum.QPE._scaled_delta_b_is_zero_or_non_int