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 A, Conditional, ExprRange, ExprTuple, Function, IndexedVar, K, Lambda, V, Variable, W, n, v
from proveit.core_expr_types import A_1_to_n, V_1_to_n, W_1_to_n, v_1_to_n
from proveit.linear_algebra import LinMap, TensorProd, VecSpaces
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [V_1_to_n, W_1_to_n], instance_expr = Forall(instance_param_or_params = [A_1_to_n], instance_expr = Forall(instance_param_or_params = [v_1_to_n], instance_expr = Equals(Function(TensorProd(A_1_to_n), [TensorProd(v_1_to_n)]), TensorProd(ExprRange(sub_expr1, Function(IndexedVar(A, sub_expr1), [IndexedVar(v, sub_expr1)]), one, n))), domains = [V_1_to_n]).with_wrapping(), domains = [ExprRange(sub_expr1, LinMap(IndexedVar(V, sub_expr1), IndexedVar(W, sub_expr1)), one, n)]).with_wrapping(), domain = VecSpaces(K)).with_wrapping(), InSet(n, NaturalPos))))

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(n \mapsto \left\{\begin{array}{l}\forall_{V_{1}, V_{2}, \ldots, V_{n}, W_{1}, W_{2}, \ldots, W_{n} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\left[\begin{array}{l}\forall_{\left(A_{1} \in \mathcal{L}\left(V_{1}, W_{1}\right)\right), \left(A_{2} \in \mathcal{L}\left(V_{2}, W_{2}\right)\right), \ldots, \left(A_{n} \in \mathcal{L}\left(V_{n}, W_{n}\right)\right)}~\\
\left[\begin{array}{l}\forall_{\left(v_{1} \in V_{1}\right), \left(v_{2} \in V_{2}\right), \ldots, \left(v_{n} \in V_{n}\right)}~\\
\left(\left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{n}\right)\left(v_{1} {\otimes}  v_{2} {\otimes}  \ldots {\otimes}  v_{n}\right) = \left(A_{1}\left(v_{1}\right) {\otimes}  A_{2}\left(v_{2}\right) {\otimes}  \ldots {\otimes}  A_{n}\left(v_{n}\right)\right)\right)\end{array}\right]\end{array}\right]\end{array} \textrm{ if } n \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	parameter: 80 body: 3
2	ExprTuple	80
3	Conditional	value: 4 condition: 5
4	Operation	operator: 30 operand: 8
5	Operation	operator: 71 operands: 7
6	ExprTuple	8
7	ExprTuple	80, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 13
11	Conditional	value: 14 condition: 15
12	ExprRange	lambda_map: 16 start_index: 79 end_index: 80
13	ExprRange	lambda_map: 17 start_index: 79 end_index: 80
14	Operation	operator: 30 operand: 20
15	Operation	operator: 49 operands: 19
16	Lambda	parameter: 88 body: 77
17	Lambda	parameter: 88 body: 66
18	ExprTuple	20
19	ExprTuple	21, 22
20	Lambda	parameters: 62 body: 23
21	ExprRange	lambda_map: 24 start_index: 79 end_index: 80
22	ExprRange	lambda_map: 25 start_index: 79 end_index: 80
23	Conditional	value: 26 condition: 27
24	Lambda	parameter: 88 body: 28
25	Lambda	parameter: 88 body: 29
26	Operation	operator: 30 operand: 36
27	Operation	operator: 49 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36
32	ExprTuple	37
33	ExprTuple	77, 38
34	Literal
35	ExprTuple	66, 38
36	Lambda	parameters: 69 body: 39
37	ExprRange	lambda_map: 40 start_index: 79 end_index: 80
38	Operation	operator: 41 operand: 46
39	Conditional	value: 43 condition: 44
40	Lambda	parameter: 88 body: 45
41	Literal
42	ExprTuple	46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operands: 50
45	Operation	operator: 71 operands: 51
46	Variable
47	Literal
48	ExprTuple	52, 53
49	Literal
50	ExprTuple	54
51	ExprTuple	81, 55
52	Operation	operator: 56 operand: 63
53	Operation	operator: 68 operands: 58
54	ExprRange	lambda_map: 59 start_index: 79 end_index: 80
55	Operation	operator: 60 operands: 61
56	Operation	operator: 68 operands: 62
57	ExprTuple	63
58	ExprTuple	64
59	Lambda	parameter: 88 body: 65
60	Literal
61	ExprTuple	77, 66
62	ExprTuple	67
63	Operation	operator: 68 operands: 69
64	ExprRange	lambda_map: 70 start_index: 79 end_index: 80
65	Operation	operator: 71 operands: 72
66	IndexedVar	variable: 73 index: 88
67	ExprRange	lambda_map: 74 start_index: 79 end_index: 80
68	Literal
69	ExprTuple	75
70	Lambda	parameter: 88 body: 76
71	Literal
72	ExprTuple	85, 77
73	Variable
74	Lambda	parameter: 88 body: 81
75	ExprRange	lambda_map: 78 start_index: 79 end_index: 80
76	Operation	operator: 81 operand: 85
77	IndexedVar	variable: 83 index: 88
78	Lambda	parameter: 88 body: 85
79	Literal
80	Variable
81	IndexedVar	variable: 84 index: 88
82	ExprTuple	85
83	Variable
84	Variable
85	IndexedVar	variable: 86 index: 88
86	Variable
87	ExprTuple	88
88	Variable