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 Conditional, ExprTuple, K, Lambda, i, j, k
from proveit.core_expr_types import U_1_to_i, V_1_to_j, W_1_to_k, a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [U_1_to_i, V_1_to_j, W_1_to_k]
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Equals(TensorProd(a_1_to_i, b_1_to_j, c_1_to_k), TensorProd(a_1_to_i, TensorProd(b_1_to_j), c_1_to_k)).with_wrapping_at(2), domains = sub_expr1).with_wrapping(), domain = VecSpaces(K)).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, 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, k\right) \mapsto \left\{\begin{array}{l}\forall_{U_{1}, U_{2}, \ldots, U_{i}, V_{1}, V_{2}, \ldots, V_{j}, W_{1}, W_{2}, \ldots, W_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\left[\begin{array}{l}\forall_{\left(a_{1} \in U_{1}\right), \left(a_{2} \in U_{2}\right), \ldots, \left(a_{i} \in U_{i}\right),\left(b_{1} \in V_{1}\right), \left(b_{2} \in V_{2}\right), \ldots, \left(b_{j} \in V_{j}\right),\left(c_{1} \in W_{1}\right), \left(c_{2} \in W_{2}\right), \ldots, \left(c_{k} \in W_{k}\right)}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}{\otimes} b_{1} {\otimes}  b_{2} {\otimes}  \ldots {\otimes}  b_{j}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} {\otimes}  b_{2} {\otimes}  \ldots {\otimes}  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \end{array} \end{array}\right)\end{array}\right]\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \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	71, 88, 75
3	Conditional	value: 4 condition: 5
4	Operation	operator: 26 operand: 8
5	Operation	operator: 44 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 78 operands: 14
10	Operation	operator: 78 operands: 15
11	Operation	operator: 78 operands: 16
12	ExprTuple	17, 18, 19
13	Conditional	value: 20 condition: 21
14	ExprTuple	71, 22
15	ExprTuple	88, 22
16	ExprTuple	75, 22
17	ExprRange	lambda_map: 23 start_index: 87 end_index: 71
18	ExprRange	lambda_map: 24 start_index: 87 end_index: 88
19	ExprRange	lambda_map: 25 start_index: 87 end_index: 75
20	Operation	operator: 26 operand: 29
21	Operation	operator: 44 operands: 28
22	Literal
23	Lambda	parameter: 97 body: 82
24	Lambda	parameter: 97 body: 83
25	Lambda	parameter: 97 body: 85
26	Literal
27	ExprTuple	29
28	ExprTuple	30, 31, 32
29	Lambda	parameters: 56 body: 33
30	ExprRange	lambda_map: 34 start_index: 87 end_index: 71
31	ExprRange	lambda_map: 35 start_index: 87 end_index: 88
32	ExprRange	lambda_map: 36 start_index: 87 end_index: 75
33	Conditional	value: 37 condition: 38
34	Lambda	parameter: 97 body: 39
35	Lambda	parameter: 97 body: 40
36	Lambda	parameter: 97 body: 41
37	Operation	operator: 42 operands: 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 48 operands: 46
40	Operation	operator: 48 operands: 47
41	Operation	operator: 48 operands: 49
42	Literal
43	ExprTuple	50, 51
44	Literal
45	ExprTuple	52, 53, 54
46	ExprTuple	82, 55
47	ExprTuple	83, 55
48	Literal
49	ExprTuple	85, 55
50	Operation	operator: 72 operands: 56
51	Operation	operator: 72 operands: 57
52	ExprRange	lambda_map: 58 start_index: 87 end_index: 71
53	ExprRange	lambda_map: 59 start_index: 87 end_index: 88
54	ExprRange	lambda_map: 60 start_index: 87 end_index: 75
55	Operation	operator: 61 operand: 69
56	ExprTuple	63, 80, 65
57	ExprTuple	63, 64, 65
58	Lambda	parameter: 97 body: 66
59	Lambda	parameter: 97 body: 67
60	Lambda	parameter: 97 body: 68
61	Literal
62	ExprTuple	69
63	ExprRange	lambda_map: 70 start_index: 87 end_index: 71
64	Operation	operator: 72 operands: 73
65	ExprRange	lambda_map: 74 start_index: 87 end_index: 75
66	Operation	operator: 78 operands: 76
67	Operation	operator: 78 operands: 77
68	Operation	operator: 78 operands: 79
69	Variable
70	Lambda	parameter: 97 body: 81
71	Variable
72	Literal
73	ExprTuple	80
74	Lambda	parameter: 97 body: 84
75	Variable
76	ExprTuple	81, 82
77	ExprTuple	94, 83
78	Literal
79	ExprTuple	84, 85
80	ExprRange	lambda_map: 86 start_index: 87 end_index: 88
81	IndexedVar	variable: 89 index: 97
82	IndexedVar	variable: 90 index: 97
83	IndexedVar	variable: 91 index: 97
84	IndexedVar	variable: 92 index: 97
85	IndexedVar	variable: 93 index: 97
86	Lambda	parameter: 97 body: 94
87	Literal
88	Variable
89	Variable
90	Variable
91	Variable
92	Variable
93	Variable
94	IndexedVar	variable: 95 index: 97
95	Variable
96	ExprTuple	97
97	Variable