Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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