Expression of type Conditional

from the theory of proveit.numbers.modular

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.
%load_expr # Load the stored expression as 'stored_expr'
# 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 LessEq, ModAbs, Real, RealPos, frac, two, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(ModAbs(x, N), x), And(InSet(x, Real), InSet(N, RealPos), And(LessEq(zero, x), LessEq(x, frac(N, two))).with_total_ordering_style()))

expr:

# 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

# 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} = x \textrm{ if } x \in \mathbb{R} ,  N \in \mathbb{R}^+ ,  0 \leq x \leq \frac{N}{2}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6, 25
5	ExprTuple	7, 8, 9
6	Operation	operator: 10 operands: 11
7	Operation	operator: 13 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	Literal
11	ExprTuple	25, 29
12	ExprTuple	25, 17
13	Literal
14	ExprTuple	29, 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	Literal
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	25, 26
24	Literal
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Variable
30	Literal