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Theorem Dependencies

proveit.logic.sets.inclusion.relax_proper_subset

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.logic.sets.inclusion import relax_proper_subset
In [2]:
%dependencies relax_proper_subset

Axioms required (directly or indirectly) to prove relax_proper_subset

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

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

proveit.logic.sets.inclusion.proper_subset_def

Theorems/conjectures that depend directly on relax_proper_subset

proveit.logic.booleans.disjunction.closure
proveit.numbers.exponentiation.sqrt2_is_not_rational
proveit.numbers.ordering.max_nat_n_zero_is_n
proveit.numbers.ordering.min_nat_n_zero_is_zero
proveit.numbers.summation.finite_geom_sum
proveit.numbers.summation.sum_first_n_int
proveit.physics.quantum.QPE._Psi_output
proveit.physics.quantum.QPE._alpha_ideal_case
proveit.physics.quantum.QPE._alpha_m_evaluation
proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
proveit.physics.quantum.QPE._alpha_summed
proveit.physics.quantum.QPE._best_guarantee
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._e_value_ge_two
proveit.physics.quantum.QPE._e_value_in_e_domain
proveit.physics.quantum.QPE._fail_sum
proveit.physics.quantum.QPE._fail_sum_prob_conds_equiv_lemma
proveit.physics.quantum.QPE._failure_upper_bound
proveit.physics.quantum.QPE._failure_upper_bound_lemma
proveit.physics.quantum.QPE._modabs_in_full_domain_simp
proveit.physics.quantum.QPE._non_int_delta_b_diff
proveit.physics.quantum.QPE._outcome_prob
proveit.physics.quantum.QPE._precision_guarantee_lemma_01
proveit.physics.quantum.QPE._precision_guarantee_lemma_02
proveit.physics.quantum.QPE._psi_t_formula
proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
proveit.physics.quantum.QPE._psi_t_output
proveit.physics.quantum.QPE._sample_space_bijection
proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
proveit.physics.quantum.QPE.qpe_best_guarantee