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 Abs, LessEq, ModAbs, Real, RealPos, frac, two

# 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:

# 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} = \left|x\right| \textrm{ if } x \in \mathbb{R} ,  N \in \mathbb{R}^+ ,  \left|x\right| \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: 5 operands: 6
3	Literal
4	ExprTuple	7, 20
5	Literal
6	ExprTuple	8, 9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	26, 27
13	ExprTuple	26, 18
14	Literal
15	ExprTuple	27, 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Literal
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Literal