Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, Q, V, f, i, j, k
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import TensorProd, VecSpaces, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Natural, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)
expr = ExprTuple(Lambda([K, f, Q], Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a_1_to_i, c_1_to_k], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, V), condition = Q__b_1_to_j), Equals(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, condition = Q__b_1_to_j), TensorProd(a_1_to_i, vec_summation_b1toj_fQ, c_1_to_k)).with_wrapping_at(1)).with_wrapping_at(2)), domain = VecSpaces(K)), domains = [Natural, NaturalPos, 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(K, f, Q\right) \mapsto \left[\forall_{i \in \mathbb{N}, j \in \mathbb{N}^+, k \in \mathbb{N}}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right] \\  = \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \end{array} \end{array}\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	parameters: 2 body: 3
2	ExprTuple	37, 72, 73
3	Operation	operator: 40 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	69, 82, 71
7	Conditional	value: 8 condition: 9
8	Operation	operator: 40 operand: 13
9	Operation	operator: 11 operands: 12
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15, 16
13	Lambda	parameter: 58 body: 18
14	Operation	operator: 53 operands: 19
15	Operation	operator: 53 operands: 20
16	Operation	operator: 53 operands: 21
17	ExprTuple	58
18	Conditional	value: 22 condition: 23
19	ExprTuple	69, 25
20	ExprTuple	82, 24
21	ExprTuple	71, 25
22	Operation	operator: 40 operand: 29
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	58, 30
29	Lambda	parameters: 31 body: 32
30	Operation	operator: 33 operand: 37
31	ExprTuple	64, 65
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Operation	operator: 40 operand: 44
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	44
42	Literal
43	ExprTuple	45, 46
44	Lambda	parameters: 74 body: 47
45	Operation	operator: 56 operand: 51
46	Operation	operator: 61 operands: 49
47	Conditional	value: 50 condition: 67
48	ExprTuple	51
49	ExprTuple	64, 52, 65
50	Operation	operator: 53 operands: 54
51	Lambda	parameters: 74 body: 55
52	Operation	operator: 56 operand: 60
53	Literal
54	ExprTuple	59, 58
55	Conditional	value: 59 condition: 67
56	Literal
57	ExprTuple	60
58	Variable
59	Operation	operator: 61 operands: 62
60	Lambda	parameters: 74 body: 63
61	Literal
62	ExprTuple	64, 66, 65
63	Conditional	value: 66 condition: 67
64	ExprRange	lambda_map: 68 start_index: 81 end_index: 69
65	ExprRange	lambda_map: 70 start_index: 81 end_index: 71
66	Operation	operator: 72 operands: 74
67	Operation	operator: 73 operands: 74
68	Lambda	parameter: 86 body: 75
69	Variable
70	Lambda	parameter: 86 body: 76
71	Variable
72	Variable
73	Variable
74	ExprTuple	77
75	IndexedVar	variable: 78 index: 86
76	IndexedVar	variable: 79 index: 86
77	ExprRange	lambda_map: 80 start_index: 81 end_index: 82
78	Variable
79	Variable
80	Lambda	parameter: 86 body: 83
81	Literal
82	Variable
83	IndexedVar	variable: 84 index: 86
84	Variable
85	ExprTuple	86
86	Variable