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, RealPos

# build up the expression from sub-expressions
expr = Lambda(L, Conditional(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), 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(\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} \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: 30 body: 2
1	ExprTuple	30
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	30, 11
9	Operation	operator: 22 operands: 12
10	Operation	operator: 22 operands: 13
11	Literal
12	ExprTuple	14, 30
13	ExprTuple	15, 30
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	20, 19, 21
17	Literal
18	ExprTuple	20, 29, 21
19	Operation	operator: 22 operands: 23
20	ExprRange	lambda_map: 24 start_index: 27 end_index: 25
21	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
22	Literal
23	ExprTuple	29, 30
24	Lambda	parameter: 36 body: 31
25	Variable
26	Lambda	parameter: 36 body: 32
27	Literal
28	Variable
29	Variable
30	Variable
31	IndexedVar	variable: 33 index: 36
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable