Theorem Dependencies¶

proveit.numbers.ordering.max_y_ge_x ¶

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 max_y_ge_x

In [2]:

%dependencies max_y_ge_x

Unproven conjectures required (directly or indirectly) to prove max_y_ge_x

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.numbers.numerals.decimals.add_1_1

proveit.numbers.numerals.decimals.tuple_len_2_typical_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

Axioms required (directly or indirectly) to prove max_y_ge_x

proveit.core_expr_types.conditionals.true_case_reduction

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

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

proveit.numbers.ordering.max_def_bin

No theorems/conjectures depend upon max_y_ge_x