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, 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
from proveit.numbers import NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [n], instance_expr = 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(), domain = 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(K \mapsto \left[\forall_{n \in \mathbb{N}^+}~\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}\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: 49 body: 2
2	Operation	operator: 33 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 83 body: 6
5	ExprTuple	83
6	Conditional	value: 7 condition: 8
7	Operation	operator: 33 operand: 11
8	Operation	operator: 74 operands: 10
9	ExprTuple	11
10	ExprTuple	83, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	15, 16
14	Conditional	value: 17 condition: 18
15	ExprRange	lambda_map: 19 start_index: 82 end_index: 83
16	ExprRange	lambda_map: 20 start_index: 82 end_index: 83
17	Operation	operator: 33 operand: 23
18	Operation	operator: 52 operands: 22
19	Lambda	parameter: 91 body: 80
20	Lambda	parameter: 91 body: 69
21	ExprTuple	23
22	ExprTuple	24, 25
23	Lambda	parameters: 65 body: 26
24	ExprRange	lambda_map: 27 start_index: 82 end_index: 83
25	ExprRange	lambda_map: 28 start_index: 82 end_index: 83
26	Conditional	value: 29 condition: 30
27	Lambda	parameter: 91 body: 31
28	Lambda	parameter: 91 body: 32
29	Operation	operator: 33 operand: 39
30	Operation	operator: 52 operands: 35
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	ExprTuple	39
35	ExprTuple	40
36	ExprTuple	80, 41
37	Literal
38	ExprTuple	69, 41
39	Lambda	parameters: 72 body: 42
40	ExprRange	lambda_map: 43 start_index: 82 end_index: 83
41	Operation	operator: 44 operand: 49
42	Conditional	value: 46 condition: 47
43	Lambda	parameter: 91 body: 48
44	Literal
45	ExprTuple	49
46	Operation	operator: 50 operands: 51
47	Operation	operator: 52 operands: 53
48	Operation	operator: 74 operands: 54
49	Variable
50	Literal
51	ExprTuple	55, 56
52	Literal
53	ExprTuple	57
54	ExprTuple	84, 58
55	Operation	operator: 59 operand: 66
56	Operation	operator: 71 operands: 61
57	ExprRange	lambda_map: 62 start_index: 82 end_index: 83
58	Operation	operator: 63 operands: 64
59	Operation	operator: 71 operands: 65
60	ExprTuple	66
61	ExprTuple	67
62	Lambda	parameter: 91 body: 68
63	Literal
64	ExprTuple	80, 69
65	ExprTuple	70
66	Operation	operator: 71 operands: 72
67	ExprRange	lambda_map: 73 start_index: 82 end_index: 83
68	Operation	operator: 74 operands: 75
69	IndexedVar	variable: 76 index: 91
70	ExprRange	lambda_map: 77 start_index: 82 end_index: 83
71	Literal
72	ExprTuple	78
73	Lambda	parameter: 91 body: 79
74	Literal
75	ExprTuple	88, 80
76	Variable
77	Lambda	parameter: 91 body: 84
78	ExprRange	lambda_map: 81 start_index: 82 end_index: 83
79	Operation	operator: 84 operand: 88
80	IndexedVar	variable: 86 index: 91
81	Lambda	parameter: 91 body: 88
82	Literal
83	Variable
84	IndexedVar	variable: 87 index: 91
85	ExprTuple	88
86	Variable
87	Variable
88	IndexedVar	variable: 89 index: 91
89	Variable
90	ExprTuple	91
91	Variable