# 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 Conditional, N, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, LessEq, ModAbs, Real, RealPos, frac, two

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Abs(x)
expr = Conditional(Equals(ModAbs(x, N), sub_expr1), And(InSet(x, Real), InSet(N, RealPos), LessEq(sub_expr1, 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\{\left|x\right|_{\textup{mod}\thinspace N} = \left|x\right| \textrm{ if } 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
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: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 20
5Literal
6ExprTuple8, 9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple26, 27
13ExprTuple26, 18
14Literal
15ExprTuple27, 19
16Literal
17ExprTuple20, 21
18Literal
19Literal
20Operationoperator: 22
operand: 26
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple26
24Literal
25ExprTuple27, 28
26Variable
27Variable
28Literal