# 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 N, x
from proveit.logic import Equals, Forall
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 = Forall(instance_param_or_params = [x, N], instance_expr = Equals(ModAbs(x, N), sub_expr1), domains = [Real, RealPos], condition = 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())

\forall_{x \in \mathbb{R}, N \in \mathbb{R}^+~|~\left|x\right| \leq \frac{N}{2}}~\left(\left|x\right|_{\textup{mod}\thinspace N} = \left|x\right|\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 16
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 24
9Literal
10ExprTuple12, 13, 14
11Operationoperator: 15
operands: 16
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14Operationoperator: 20
operands: 21
15Literal
16ExprTuple30, 31
17ExprTuple30, 22
18Literal
19ExprTuple31, 23
20Literal
21ExprTuple24, 25
22Literal
23Literal
24Operationoperator: 26
operand: 30
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple30
28Literal
29ExprTuple31, 32
30Variable
31Variable
32Literal