Theorem Dependencies

proveit.numbers.divisibility.non_zero_divides_zero

see proof

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.divisibility import non_zero_divides_zero

%dependencies non_zero_divides_zero

Unproven conjectures required (directly or indirectly) to prove non_zero_divides_zero

proveit.numbers.division.frac_zero_numer

proveit.numbers.number_sets.integers.nat_within_int

Axioms required (directly or indirectly) to prove non_zero_divides_zero

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

proveit.logic.sets.inclusion.proper_subset_def

proveit.logic.sets.inclusion.subset_eq_def

proveit.numbers.number_sets.natural_numbers.zero_in_nats

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

proveit.numbers.divisibility.divides_def

No theorems/conjectures depend upon non_zero_divides_zero