# from the theory of proveit.numbers.number_sets.integers¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, a
from proveit.logic import And, InSet
from proveit.numbers import Integer, Natural, greater_eq, zero

In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(a, Natural), And(InSet(a, Integer), greater_eq(a, zero)))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{a \in \mathbb{N} \textrm{ if } a \in \mathbb{Z} ,  a \geq 0\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 9
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple15, 6
4Literal
5ExprTuple7, 8
6Literal
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operands: 12
9Literal
10ExprTuple15, 13
11Literal
12ExprTuple14, 15
13Literal
14Literal
15Variable