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 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(alpha, Conditional(Forall(instance_param_or_params = [i, k], instance_expr = 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(), domain = Natural), InSet(alpha, K))))

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