Axioms for the theory of proveit.numbers.numerals.binaries

import proveit

# Prepare this notebook for defining the axioms of a theory:
%axioms_notebook # Keep this at the top following 'import proveit'.
from proveit import b
from proveit.logic import Forall, Equals
from proveit.numbers import Bit, BinarySequence

%begin axioms

Defining axioms for theory 'proveit.numbers.numerals.binaries'
Subsequent end-of-cell assignments will define axioms
%end_axioms will finalize the definitions

single_bit_reduction = Forall(b, Equals(BinarySequence(b), b), 
                              domain=Bit)

single_bit_reduction:

%end axioms

These axioms may now be imported from the theory package: proveit.numbers.numerals.binaries