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Theorem Dependencies

proveit.logic.equality.sub_left_side_into

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.equality import sub_left_side_into
In [2]:
%dependencies sub_left_side_into

Axioms required (directly or indirectly) to prove sub_left_side_into

proveit.logic.booleans.eq_true_elim
proveit.logic.booleans.eq_true_intro
proveit.logic.equality.equals_transitivity
proveit.logic.equality.substitution

Theorems/conjectures that depend directly on sub_left_side_into

proveit.logic.booleans.disjunction.closure
proveit.logic.booleans.fold_is_bool
proveit.logic.booleans.forall_over_bool_by_cases
proveit.logic.booleans.implication.not_iff_via_not_left_impl
proveit.logic.booleans.implication.not_iff_via_not_right_impl
proveit.logic.booleans.in_bool_def
proveit.logic.booleans.in_bool_is_bool
proveit.logic.booleans.negation.closure
proveit.logic.booleans.negation.negation_intro
proveit.logic.equality.lhs_via_equality
proveit.logic.equality.not_equals_is_bool
proveit.logic.equality.not_equals_symmetry
proveit.logic.equality.sub_right_side_into
proveit.logic.equality.substitute_falsehood
proveit.logic.equality.substitute_truth
proveit.logic.sets.comprehension.fold
proveit.logic.sets.comprehension.unfold
proveit.logic.sets.enumeration.in_singleton_eval_false
proveit.logic.sets.enumeration.in_singleton_eval_true
proveit.logic.sets.enumeration.in_singleton_is_bool
proveit.logic.sets.equivalence.set_equiv_is_bool
proveit.logic.sets.equivalence.set_not_equiv_is_bool
proveit.logic.sets.equivalence.set_not_equiv_reversal
proveit.logic.sets.membership.not_in_set_is_bool
proveit.numbers.divisibility.divides_is_bool
proveit.numbers.divisibility.non_zero_divides_zero
proveit.numbers.exponentiation.sqrt2_is_not_rational
proveit.numbers.ordering.max_bin_args_commute
proveit.numbers.ordering.min_bin_args_commute
proveit.numbers.ordering.min_nat_n_zero_is_zero
proveit.numbers.ordering.min_y_le_x
proveit.numbers.ordering.transitivity_less_eq_less
proveit.numbers.ordering.transitivity_less_eq_less_eq
proveit.numbers.summation.finite_geom_sum
proveit.numbers.summation.sum_first_n_int
proveit.physics.quantum.QPE._Psi_output
proveit.physics.quantum.QPE._alpha_are_complex
proveit.physics.quantum.QPE._alpha_m_evaluation
proveit.physics.quantum.QPE._alpha_m_mod_as_geometric_sum
proveit.physics.quantum.QPE._alpha_m_mod_evaluation
proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
proveit.physics.quantum.QPE._alpha_summed
proveit.physics.quantum.QPE._best_floor_is_in_m_domain
proveit.physics.quantum.QPE._best_floor_is_int
proveit.physics.quantum.QPE._best_guarantee
proveit.physics.quantum.QPE._best_guarantee_delta_nonzero
proveit.physics.quantum.QPE._best_round_is_int
proveit.physics.quantum.QPE._delta_b_is_real
proveit.physics.quantum.QPE._delta_b_is_zero_or_non_int
proveit.physics.quantum.QPE._fail_sum
proveit.physics.quantum.QPE._fail_sum_prob_conds_equiv_lemma
proveit.physics.quantum.QPE._failure_upper_bound_lemma
proveit.physics.quantum.QPE._mod_add_closure
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._pfail_in_real
proveit.physics.quantum.QPE._precision_guarantee
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_is_zero_or_non_int
proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
proveit.physics.quantum.QPE.qpe_best_guarantee