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, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Mod, ModAbs, Natural, Real, RealPos

# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = Forall(instance_param_or_params = [L], instance_expr = 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), domain = RealPos), domain = Real), And(InSet(i, Natural), InSet(j, Natural))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}}~\left[\forall_{L \in \mathbb{R}^+}~\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}\right)\right] \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	57, 60
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 7
4	Operation	operator: 18 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 50 body: 10
8	Operation	operator: 37 operands: 11
9	Operation	operator: 37 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	57, 15
12	ExprTuple	60, 15
13	Operation	operator: 16 operand: 20
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	21, 22, 23
20	Lambda	parameter: 62 body: 25
21	ExprRange	lambda_map: 26 start_index: 59 end_index: 57
22	Operation	operator: 37 operands: 27
23	ExprRange	lambda_map: 28 start_index: 59 end_index: 60
24	ExprTuple	62
25	Conditional	value: 29 condition: 30
26	Lambda	parameter: 68 body: 31
27	ExprTuple	61, 42
28	Lambda	parameter: 68 body: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 37 operands: 35
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	ExprTuple	39, 40
35	ExprTuple	62, 41
36	ExprTuple	63, 42
37	Literal
38	ExprTuple	64, 42
39	Operation	operator: 44 operands: 43
40	Operation	operator: 44 operands: 45
41	Literal
42	Literal
43	ExprTuple	46, 62
44	Literal
45	ExprTuple	47, 62
46	Operation	operator: 49 operands: 48
47	Operation	operator: 49 operands: 50
48	ExprTuple	52, 51, 53
49	Literal
50	ExprTuple	52, 61, 53
51	Operation	operator: 54 operands: 55
52	ExprRange	lambda_map: 56 start_index: 59 end_index: 57
53	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
54	Literal
55	ExprTuple	61, 62
56	Lambda	parameter: 68 body: 63
57	Variable
58	Lambda	parameter: 68 body: 64
59	Literal
60	Variable
61	Variable
62	Variable
63	IndexedVar	variable: 65 index: 68
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable