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

# build up the expression from sub-expressions
expr = Conditional(Equals(ModAbs(Add(a_1_to_i, Mod(b, L), c_1_to_j), L), ModAbs(Add(a_1_to_i, b, c_1_to_j), L)).with_wrapping_at(2), InSet(L, RealPos))

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\{\begin{array}{c} \begin{array}{l} \left|a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b ~\textup{mod}~ L\right)+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} =  \\ \left|a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right|_{\textup{mod}\thinspace L} \end{array} \end{array} \textrm{ if } L \in \mathbb{R}^+\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, 8
5	Literal
6	ExprTuple	29, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 29
11	Literal
12	ExprTuple	14, 29
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	19, 18, 20
16	Literal
17	ExprTuple	19, 28, 20
18	Operation	operator: 21 operands: 22
19	ExprRange	lambda_map: 23 start_index: 26 end_index: 24
20	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
21	Literal
22	ExprTuple	28, 29
23	Lambda	parameter: 35 body: 30
24	Variable
25	Lambda	parameter: 35 body: 31
26	Literal
27	Variable
28	Variable
29	Variable
30	IndexedVar	variable: 32 index: 35
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable