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Theorem Dependencies

proveit.physics.quantum.QPE._modabs_in_full_domain_simp

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 _modabs_in_full_domain_simp
In [2]:
%dependencies _modabs_in_full_domain_simp

Unproven conjectures required (directly or indirectly) to prove _modabs_in_full_domain_simp

proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
proveit.core_expr_types.conditionals.satisfied_condition_reduction
proveit.core_expr_types.tuples.tuple_len_0_typical_eq
proveit.logic.equality.four_chain_transitivity
proveit.numbers.absolute_value.abs_neg_elim
proveit.numbers.absolute_value.abs_non_neg_elim
proveit.numbers.absolute_value.weak_upper_bound_asym_interval
proveit.numbers.addition.add_int_closure_bin
proveit.numbers.addition.commutation
proveit.numbers.addition.disassociation
proveit.numbers.addition.elim_zero_any
proveit.numbers.addition.strong_bound_via_left_term_bound
proveit.numbers.addition.subtraction.add_cancel_basic
proveit.numbers.addition.subtraction.add_cancel_triple_13
proveit.numbers.addition.subtraction.nonneg_difference
proveit.numbers.addition.weak_bound_via_left_term_bound
proveit.numbers.division.div_as_mult
proveit.numbers.division.div_complex_closure
proveit.numbers.exponentiation.complex_x_to_first_power_is_x
proveit.numbers.exponentiation.exp_complex_closure
proveit.numbers.exponentiation.exp_natpos_closure
proveit.numbers.exponentiation.neg_power_as_div
proveit.numbers.exponentiation.product_of_real_powers
proveit.numbers.multiplication.commutation
proveit.numbers.multiplication.mult_complex_closure_bin
proveit.numbers.negation.distribute_neg_through_binary_sum
proveit.numbers.negation.double_negation
proveit.numbers.negation.int_closure
proveit.numbers.negation.int_neg_closure
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.int_interval_within_int
proveit.numbers.number_sets.integers.interval_lower_bound
proveit.numbers.number_sets.integers.interval_upper_bound
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_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.neg_int_within_rational_neg
proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
proveit.numbers.number_sets.real_numbers.nat_pos_within_real
proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
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_neg_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.numerals.decimals.posnat1
proveit.numbers.numerals.decimals.posnat2
proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
proveit.numbers.ordering.less_is_not_eq_nat
proveit.numbers.ordering.less_or_greater_eq
proveit.numbers.ordering.not_less_eq_from_less
proveit.numbers.ordering.not_less_from_less_eq
proveit.numbers.ordering.relax_equal_to_less_eq
proveit.numbers.ordering.relax_less

Axioms required (directly or indirectly) to prove _modabs_in_full_domain_simp

proveit.core_expr_types.conditionals.true_case_reduction
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.max_def_bin
proveit.numbers.ordering.transitivity_less_less
proveit.physics.quantum.QPE._t_in_natural_pos

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

proveit.numbers.modular.mod_abs_x_reduce_to_abs_x

Theorems/conjectures that depend directly on _modabs_in_full_domain_simp

proveit.physics.quantum.QPE._fail_sum
proveit.physics.quantum.QPE._fail_sum_prob_conds_equiv_lemma