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Theorem Dependencies

proveit.physics.quantum.QPE._precision_guarantee_lemma_01

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 _precision_guarantee_lemma_01
In [2]:
%dependencies _precision_guarantee_lemma_01

Unproven conjectures required (directly or indirectly) to prove _precision_guarantee_lemma_01

proveit.core_expr_types.operations.operands_substitution_via_tuple
proveit.core_expr_types.tuples.range_from1_len_typical_eq
proveit.core_expr_types.tuples.tuple_len_0_typical_eq
proveit.logic.equality.four_chain_transitivity
proveit.numbers.addition.add_complex_closure_bin
proveit.numbers.addition.add_int_closure_bin
proveit.numbers.addition.add_rational_closure_bin
proveit.numbers.addition.add_real_closure_bin
proveit.numbers.addition.add_real_pos_closure_bin
proveit.numbers.addition.association
proveit.numbers.addition.commutation
proveit.numbers.addition.disassociation
proveit.numbers.addition.elim_zero_any
proveit.numbers.addition.elim_zero_left
proveit.numbers.addition.leftward_commutation
proveit.numbers.addition.rational_pair_addition
proveit.numbers.addition.strong_bound_via_left_term_bound
proveit.numbers.addition.strong_bound_via_right_term_bound
proveit.numbers.addition.subtraction.add_cancel_general
proveit.numbers.addition.subtraction.add_cancel_triple_13
proveit.numbers.addition.subtraction.add_cancel_triple_23
proveit.numbers.addition.subtraction.add_cancel_triple_32
proveit.numbers.addition.subtraction.nonneg_difference
proveit.numbers.addition.subtraction.pos_difference
proveit.numbers.addition.subtraction.subtract_from_add
proveit.numbers.addition.subtraction.subtract_from_add_reversed
proveit.numbers.addition.weak_bound_via_left_term_bound
proveit.numbers.addition.weak_bound_via_right_term_bound
proveit.numbers.addition.weak_bound_via_term_bound
proveit.numbers.division.distribute_frac_through_sum
proveit.numbers.division.div_as_mult
proveit.numbers.division.div_rational_pos_closure
proveit.numbers.division.div_real_closure
proveit.numbers.division.div_real_pos_closure
proveit.numbers.division.frac_cancel_complete
proveit.numbers.division.frac_cancel_left
proveit.numbers.division.frac_one_denom
proveit.numbers.division.mult_frac_cancel_numer_left
proveit.numbers.division.prod_of_fracs
proveit.numbers.division.strong_div_from_numer_bound__pos_denom
proveit.numbers.division.weak_div_from_denom_bound__all_pos
proveit.numbers.exponentiation.complex_x_to_first_power_is_x
proveit.numbers.exponentiation.exp_complex_closure
proveit.numbers.exponentiation.exp_complex_nonzero_closure
proveit.numbers.exponentiation.exp_factored_real
proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
proveit.numbers.exponentiation.exp_nat_pos_expansion
proveit.numbers.exponentiation.exp_not_eq_zero
proveit.numbers.exponentiation.exp_pos_lesseq
proveit.numbers.exponentiation.exp_rational_nonzero_closure
proveit.numbers.exponentiation.exp_rational_pos_closure
proveit.numbers.exponentiation.exp_real_closure_nat_power
proveit.numbers.exponentiation.exp_real_pos_closure
proveit.numbers.exponentiation.exponent_log_with_same_base
proveit.numbers.exponentiation.neg_power_as_div
proveit.numbers.exponentiation.posnat_power_of_product
proveit.numbers.exponentiation.product_of_posnat_powers
proveit.numbers.exponentiation.real_power_of_product
proveit.numbers.exponentiation.sqrd_pos_closure
proveit.numbers.logarithms.log_eq_1
proveit.numbers.logarithms.log_increasing_less
proveit.numbers.logarithms.log_increasing_less_eq
proveit.numbers.logarithms.log_real_pos_real_closure
proveit.numbers.multiplication.association
proveit.numbers.multiplication.commutation
proveit.numbers.multiplication.disassociation
proveit.numbers.multiplication.distribute_through_sum
proveit.numbers.multiplication.elim_one_any
proveit.numbers.multiplication.elim_one_left
proveit.numbers.multiplication.elim_one_right
proveit.numbers.multiplication.leftward_commutation
proveit.numbers.multiplication.mult_complex_closure_bin
proveit.numbers.multiplication.mult_not_eq_zero
proveit.numbers.multiplication.mult_rational_closure_bin
proveit.numbers.multiplication.mult_rational_pos_closure_bin
proveit.numbers.multiplication.mult_real_closure_bin
proveit.numbers.multiplication.mult_real_pos_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.complex_closure
proveit.numbers.negation.distribute_neg_through_binary_sum
proveit.numbers.negation.int_closure
proveit.numbers.negation.int_neg_closure
proveit.numbers.negation.negated_strong_bound
proveit.numbers.negation.negated_weak_bound
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.complex_numbers.zero_is_complex
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.integers.neg_int_within_int
proveit.numbers.number_sets.integers.nonneg_int_is_natural
proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
proveit.numbers.number_sets.natural_numbers.natural_lower_bound
proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
proveit.numbers.number_sets.rational_numbers.int_within_rational
proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero
proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos
proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
proveit.numbers.number_sets.real_numbers.nat_pos_within_real
proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
proveit.numbers.number_sets.real_numbers.rational_within_real
proveit.numbers.number_sets.real_numbers.real_pos_within_real
proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
proveit.numbers.number_sets.real_numbers.zero_is_real
proveit.numbers.numerals.decimals.add_1_1
proveit.numbers.numerals.decimals.add_1_3
proveit.numbers.numerals.decimals.add_1_4
proveit.numbers.numerals.decimals.add_2_1
proveit.numbers.numerals.decimals.add_2_2
proveit.numbers.numerals.decimals.add_4_1
proveit.numbers.numerals.decimals.less_0_1
proveit.numbers.numerals.decimals.less_1_2
proveit.numbers.numerals.decimals.mult_2_2
proveit.numbers.numerals.decimals.nat3
proveit.numbers.numerals.decimals.nat4
proveit.numbers.numerals.decimals.posnat1
proveit.numbers.numerals.decimals.posnat2
proveit.numbers.numerals.decimals.posnat4
proveit.numbers.numerals.decimals.posnat5
proveit.numbers.numerals.decimals.reduce_2_repeats
proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
proveit.numbers.ordering.less_eq_add_right
proveit.numbers.ordering.less_eq_add_right_strong
proveit.numbers.ordering.less_is_not_eq
proveit.numbers.ordering.less_is_not_eq_nat
proveit.numbers.ordering.relax_less
proveit.numbers.rounding.ceil_increasing_less_eq
proveit.numbers.rounding.ceil_of_real_above_int
proveit.numbers.rounding.ceil_x_ge_x

Axioms required (directly or indirectly) to prove _precision_guarantee_lemma_01

proveit.core_expr_types.operations.operands_substitution
proveit.logic.booleans.bools_def
proveit.logic.booleans.conjunction.and_t_t
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.numbers.rounding.ceil_is_an_int
proveit.physics.quantum.QPE._eps_in_interval
proveit.physics.quantum.QPE._n_in_natural_pos
proveit.physics.quantum.QPE._t_in_natural_pos
proveit.physics.quantum.QPE._t_req

Theorems/conjectures that depend directly on _precision_guarantee_lemma_01

proveit.physics.quantum.QPE._precision_guarantee