Expression of type Equals

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 N, a, b
from proveit.logic import Equals
from proveit.numbers import Add, Mod, ModAbs

# build up the expression from sub-expressions
expr = Equals(ModAbs(Add(Mod(a, N), b), N), ModAbs(Add(a, b), N)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left|\left(a ~\textup{mod}~ N\right) + b\right|_{\textup{mod}\thinspace N} =  \\ \left|a + b\right|_{\textup{mod}\thinspace N} \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 18
6	Literal
7	ExprTuple	9, 18
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	17, 14
13	Operation	operator: 15 operands: 16
14	Variable
15	Literal
16	ExprTuple	17, 18
17	Variable
18	Variable