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 L, b
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import Equals
from proveit.numbers import Add, Mod

# build up the expression from sub-expressions
expr = Equals(Mod(Add(a_1_to_i, Mod(b, L), c_1_to_j), L), Mod(Add(a_1_to_i, b, c_1_to_j), L)).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_{1} +  a_{2} +  \ldots +  a_{i} + \left(b ~\textup{mod}~ L\right)+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) ~\textup{mod}~ L\right) =  \\ \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) ~\textup{mod}~ L\right) \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: 15 operands: 5
4	Operation	operator: 15 operands: 6
5	ExprTuple	7, 23
6	ExprTuple	8, 23
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	13, 12, 14
10	Literal
11	ExprTuple	13, 22, 14
12	Operation	operator: 15 operands: 16
13	ExprRange	lambda_map: 17 start_index: 20 end_index: 18
14	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
15	Literal
16	ExprTuple	22, 23
17	Lambda	parameter: 29 body: 24
18	Variable
19	Lambda	parameter: 29 body: 25
20	Literal
21	Variable
22	Variable
23	Variable
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable