# from the theory of proveit.numbers.modular¶

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 ExprTuple, N, x
from proveit.logic import InSet
from proveit.numbers import Abs, LessEq, Real, RealPos, frac, two

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(InSet(x, Real), InSet(N, RealPos), LessEq(Abs(x), frac(N, two)))

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(x \in \mathbb{R}, N \in \mathbb{R}^+, \left|x\right| \leq \frac{N}{2}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 5
operands: 4
2Operationoperator: 5
operands: 6
3Operationoperator: 7
operands: 8
4ExprTuple17, 9
5Literal
6ExprTuple18, 10
7Literal
8ExprTuple11, 12
9Literal
10Literal
11Operationoperator: 13
operand: 17
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Literal