Expression of type ExprTuple

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, ExprTuple, L, Lambda, 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 = ExprTuple(Lambda(L, 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(L \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 32 body: 3
2	ExprTuple	32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	32, 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 32
14	Literal
15	ExprTuple	17, 32
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	22, 21, 23
19	Literal
20	ExprTuple	22, 31, 23
21	Operation	operator: 24 operands: 25
22	ExprRange	lambda_map: 26 start_index: 29 end_index: 27
23	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
24	Literal
25	ExprTuple	31, 32
26	Lambda	parameter: 38 body: 33
27	Variable
28	Lambda	parameter: 38 body: 34
29	Literal
30	Variable
31	Variable
32	Variable
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable