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, 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 = ExprTuple(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(\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..\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	parameters: 2 body: 3
2	ExprTuple	58, 61
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 8
5	Operation	operator: 19 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 51 body: 11
9	Operation	operator: 38 operands: 12
10	Operation	operator: 38 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	58, 16
13	ExprTuple	61, 16
14	Operation	operator: 17 operand: 21
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22, 23, 24
21	Lambda	parameter: 63 body: 26
22	ExprRange	lambda_map: 27 start_index: 60 end_index: 58
23	Operation	operator: 38 operands: 28
24	ExprRange	lambda_map: 29 start_index: 60 end_index: 61
25	ExprTuple	63
26	Conditional	value: 30 condition: 31
27	Lambda	parameter: 69 body: 32
28	ExprTuple	62, 43
29	Lambda	parameter: 69 body: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 38 operands: 36
32	Operation	operator: 38 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	ExprTuple	40, 41
36	ExprTuple	63, 42
37	ExprTuple	64, 43
38	Literal
39	ExprTuple	65, 43
40	Operation	operator: 45 operands: 44
41	Operation	operator: 45 operands: 46
42	Literal
43	Literal
44	ExprTuple	47, 63
45	Literal
46	ExprTuple	48, 63
47	Operation	operator: 50 operands: 49
48	Operation	operator: 50 operands: 51
49	ExprTuple	53, 52, 54
50	Literal
51	ExprTuple	53, 62, 54
52	Operation	operator: 55 operands: 56
53	ExprRange	lambda_map: 57 start_index: 60 end_index: 58
54	ExprRange	lambda_map: 59 start_index: 60 end_index: 61
55	Literal
56	ExprTuple	62, 63
57	Lambda	parameter: 69 body: 64
58	Variable
59	Lambda	parameter: 69 body: 65
60	Literal
61	Variable
62	Variable
63	Variable
64	IndexedVar	variable: 66 index: 69
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable