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 ExprTuple, K, Lambda, V, b, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d_1_to_k], instance_expr = Equals(VecAdd(a_1_to_i, b, c_1_to_j, d_1_to_k), VecAdd(a_1_to_i, c_1_to_j, b, d_1_to_k)).with_wrapping_at(2), domain = V), domain = Natural), domain = 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(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, 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+ c_{1} +  c_{2} +  \ldots +  c_{j}+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j} + b+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) \end{array} \end{array}\right)\right]\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: 20 body: 2
2	Operation	operator: 21 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 73 body: 6
5	ExprTuple	73
6	Conditional	value: 7 condition: 8
7	Operation	operator: 21 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	73, 13
12	Lambda	parameters: 14 body: 15
13	Operation	operator: 16 operand: 20
14	ExprTuple	60, 62, 65
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operand: 24
19	Operation	operator: 37 operands: 23
20	Variable
21	Literal
22	ExprTuple	24
23	ExprTuple	25, 26, 27
24	Lambda	parameters: 45 body: 28
25	Operation	operator: 68 operands: 29
26	Operation	operator: 68 operands: 30
27	Operation	operator: 68 operands: 31
28	Conditional	value: 32 condition: 33
29	ExprTuple	60, 34
30	ExprTuple	62, 34
31	ExprTuple	65, 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42, 43, 44
39	Operation	operator: 46 operands: 45
40	Operation	operator: 46 operands: 47
41	ExprRange	lambda_map: 48 start_index: 64 end_index: 60
42	Operation	operator: 68 operands: 49
43	ExprRange	lambda_map: 50 start_index: 64 end_index: 62
44	ExprRange	lambda_map: 51 start_index: 64 end_index: 65
45	ExprTuple	52, 56, 53, 54
46	Literal
47	ExprTuple	52, 53, 56, 54
48	Lambda	parameter: 78 body: 55
49	ExprTuple	56, 73
50	Lambda	parameter: 78 body: 57
51	Lambda	parameter: 78 body: 58
52	ExprRange	lambda_map: 59 start_index: 64 end_index: 60
53	ExprRange	lambda_map: 61 start_index: 64 end_index: 62
54	ExprRange	lambda_map: 63 start_index: 64 end_index: 65
55	Operation	operator: 68 operands: 66
56	Variable
57	Operation	operator: 68 operands: 67
58	Operation	operator: 68 operands: 69
59	Lambda	parameter: 78 body: 70
60	Variable
61	Lambda	parameter: 78 body: 71
62	Variable
63	Lambda	parameter: 78 body: 72
64	Literal
65	Variable
66	ExprTuple	70, 73
67	ExprTuple	71, 73
68	Literal
69	ExprTuple	72, 73
70	IndexedVar	variable: 74 index: 78
71	IndexedVar	variable: 75 index: 78
72	IndexedVar	variable: 76 index: 78
73	Variable
74	Variable
75	Variable
76	Variable
77	ExprTuple	78
78	Variable