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 And, Equals, Forall, InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(V, sub_expr1)
sub_expr3 = IndexedVar(W, sub_expr1)
sub_expr4 = VecSpaces(K)
expr = ExprTuple(Lambda([V_1_to_n, W_1_to_n], Conditional(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(sub_expr2, sub_expr3), one, n)]).with_wrapping(), And(ExprRange(sub_expr1, InClass(sub_expr2, sub_expr4), one, n), ExprRange(sub_expr1, InClass(sub_expr3, sub_expr4), one, n)))))

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