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