Theorem Dependencies¶

proveit.numbers.ordering.transitivity_less_eq_less ¶

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

In [2]:

%dependencies transitivity_less_eq_less

Unproven conjectures required (directly or indirectly) to prove transitivity_less_eq_less

proveit.numbers.numerals.decimals.add_1_1

Axioms required (directly or indirectly) to prove transitivity_less_eq_less

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.transitivity_less_less

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

proveit.numbers.numerals.decimals.tuple_len_2_typical_eq

proveit.numbers.ordering.less_eq_def

Theorems/conjectures that depend directly on transitivity_less_eq_less

proveit.physics.quantum.QPE._alpha_sqrd_upper_bound

proveit.physics.quantum.QPE._fail_sum

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.qpe_exact