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, 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 Equals, Forall
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(K, Forall(instance_param_or_params = [i, j, k], instance_expr = 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(), domain = 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(K \mapsto \left[\forall_{i, j, k \in \mathbb{N}}~\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}\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: 72 body: 2
2	Operation	operator: 29 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	74, 91, 78
6	Conditional	value: 7 condition: 8
7	Operation	operator: 29 operand: 11
8	Operation	operator: 47 operands: 10
9	ExprTuple	11
10	ExprTuple	12, 13, 14
11	Lambda	parameters: 15 body: 16
12	Operation	operator: 81 operands: 17
13	Operation	operator: 81 operands: 18
14	Operation	operator: 81 operands: 19
15	ExprTuple	20, 21, 22
16	Conditional	value: 23 condition: 24
17	ExprTuple	74, 25
18	ExprTuple	91, 25
19	ExprTuple	78, 25
20	ExprRange	lambda_map: 26 start_index: 90 end_index: 74
21	ExprRange	lambda_map: 27 start_index: 90 end_index: 91
22	ExprRange	lambda_map: 28 start_index: 90 end_index: 78
23	Operation	operator: 29 operand: 32
24	Operation	operator: 47 operands: 31
25	Literal
26	Lambda	parameter: 100 body: 85
27	Lambda	parameter: 100 body: 86
28	Lambda	parameter: 100 body: 88
29	Literal
30	ExprTuple	32
31	ExprTuple	33, 34, 35
32	Lambda	parameters: 59 body: 36
33	ExprRange	lambda_map: 37 start_index: 90 end_index: 74
34	ExprRange	lambda_map: 38 start_index: 90 end_index: 91
35	ExprRange	lambda_map: 39 start_index: 90 end_index: 78
36	Conditional	value: 40 condition: 41
37	Lambda	parameter: 100 body: 42
38	Lambda	parameter: 100 body: 43
39	Lambda	parameter: 100 body: 44
40	Operation	operator: 45 operands: 46
41	Operation	operator: 47 operands: 48
42	Operation	operator: 51 operands: 49
43	Operation	operator: 51 operands: 50
44	Operation	operator: 51 operands: 52
45	Literal
46	ExprTuple	53, 54
47	Literal
48	ExprTuple	55, 56, 57
49	ExprTuple	85, 58
50	ExprTuple	86, 58
51	Literal
52	ExprTuple	88, 58
53	Operation	operator: 75 operands: 59
54	Operation	operator: 75 operands: 60
55	ExprRange	lambda_map: 61 start_index: 90 end_index: 74
56	ExprRange	lambda_map: 62 start_index: 90 end_index: 91
57	ExprRange	lambda_map: 63 start_index: 90 end_index: 78
58	Operation	operator: 64 operand: 72
59	ExprTuple	66, 83, 68
60	ExprTuple	66, 67, 68
61	Lambda	parameter: 100 body: 69
62	Lambda	parameter: 100 body: 70
63	Lambda	parameter: 100 body: 71
64	Literal
65	ExprTuple	72
66	ExprRange	lambda_map: 73 start_index: 90 end_index: 74
67	Operation	operator: 75 operands: 76
68	ExprRange	lambda_map: 77 start_index: 90 end_index: 78
69	Operation	operator: 81 operands: 79
70	Operation	operator: 81 operands: 80
71	Operation	operator: 81 operands: 82
72	Variable
73	Lambda	parameter: 100 body: 84
74	Variable
75	Literal
76	ExprTuple	83
77	Lambda	parameter: 100 body: 87
78	Variable
79	ExprTuple	84, 85
80	ExprTuple	97, 86
81	Literal
82	ExprTuple	87, 88
83	ExprRange	lambda_map: 89 start_index: 90 end_index: 91
84	IndexedVar	variable: 92 index: 100
85	IndexedVar	variable: 93 index: 100
86	IndexedVar	variable: 94 index: 100
87	IndexedVar	variable: 95 index: 100
88	IndexedVar	variable: 96 index: 100
89	Lambda	parameter: 100 body: 97
90	Literal
91	Variable
92	Variable
93	Variable
94	Variable
95	Variable
96	Variable
97	IndexedVar	variable: 98 index: 100
98	Variable
99	ExprTuple	100
100	Variable