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Theorem Dependencies

proveit.numbers.ordering.transitivity_less_eq_less_eq

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.numbers.ordering import transitivity_less_eq_less_eq
In [2]:
%dependencies transitivity_less_eq_less_eq

Unproven conjectures required (directly or indirectly) to prove transitivity_less_eq_less_eq

proveit.numbers.numerals.decimals.add_1_1
proveit.numbers.ordering.relax_less

Axioms required (directly or indirectly) to prove transitivity_less_eq_less_eq

proveit.logic.booleans.bools_def
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.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

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

proveit.numbers.numerals.decimals.tuple_len_2_typical_eq

Theorems/conjectures that depend directly on transitivity_less_eq_less_eq

proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
proveit.physics.quantum.QPE._delta_b_floor_diff_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._non_int_delta_b_diff
proveit.physics.quantum.QPE._precision_guarantee_lemma_01
proveit.physics.quantum.QPE._precision_guarantee_lemma_02