Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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, K, Lambda, V, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b_1_to_j, c, d_1_to_k), VecAdd(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), domain = V), domain = Natural), InClass(V, VecSpaces(K)))))

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(V \mapsto \left\{\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k} \in V}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j} + c+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + c+ b_{1} +  b_{2} +  \ldots +  b_{j}+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) \end{array} \end{array}\right)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 70 body: 3
2	ExprTuple	70
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	70, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	57, 59, 62
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operand: 21
16	Operation	operator: 34 operands: 20
17	Variable
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23, 24
21	Lambda	parameters: 42 body: 25
22	Operation	operator: 65 operands: 26
23	Operation	operator: 65 operands: 27
24	Operation	operator: 65 operands: 28
25	Conditional	value: 29 condition: 30
26	ExprTuple	57, 31
27	ExprTuple	59, 31
28	ExprTuple	62, 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39, 40, 41
36	Operation	operator: 43 operands: 42
37	Operation	operator: 43 operands: 44
38	ExprRange	lambda_map: 45 start_index: 61 end_index: 57
39	ExprRange	lambda_map: 46 start_index: 61 end_index: 59
40	Operation	operator: 65 operands: 47
41	ExprRange	lambda_map: 48 start_index: 61 end_index: 62
42	ExprTuple	49, 50, 54, 51
43	Literal
44	ExprTuple	49, 54, 50, 51
45	Lambda	parameter: 75 body: 52
46	Lambda	parameter: 75 body: 53
47	ExprTuple	54, 70
48	Lambda	parameter: 75 body: 55
49	ExprRange	lambda_map: 56 start_index: 61 end_index: 57
50	ExprRange	lambda_map: 58 start_index: 61 end_index: 59
51	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
52	Operation	operator: 65 operands: 63
53	Operation	operator: 65 operands: 64
54	Variable
55	Operation	operator: 65 operands: 66
56	Lambda	parameter: 75 body: 67
57	Variable
58	Lambda	parameter: 75 body: 68
59	Variable
60	Lambda	parameter: 75 body: 69
61	Literal
62	Variable
63	ExprTuple	67, 70
64	ExprTuple	68, 70
65	Literal
66	ExprTuple	69, 70
67	IndexedVar	variable: 71 index: 75
68	IndexedVar	variable: 72 index: 75
69	IndexedVar	variable: 73 index: 75
70	Variable
71	Variable
72	Variable
73	Variable
74	ExprTuple	75
75	Variable