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 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
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(K, Forall(instance_param_or_params = [alpha], instance_expr = 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), domain = 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(K \mapsto \left[\forall_{\alpha \in K}~\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]\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: 72 body: 2
2	Operation	operator: 32 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 80 body: 6
5	ExprTuple	80
6	Conditional	value: 7 condition: 8
7	Operation	operator: 32 operand: 11
8	Operation	operator: 78 operands: 10
9	ExprTuple	11
10	ExprTuple	80, 72
11	Lambda	parameters: 12 body: 13
12	ExprTuple	87, 90
13	Conditional	value: 14 condition: 15
14	Operation	operator: 32 operand: 18
15	Operation	operator: 49 operands: 17
16	ExprTuple	18
17	ExprTuple	19, 20
18	Lambda	parameters: 21 body: 22
19	Operation	operator: 78 operands: 23
20	Operation	operator: 78 operands: 24
21	ExprTuple	25, 70, 26
22	Conditional	value: 27 condition: 28
23	ExprTuple	87, 29
24	ExprTuple	90, 29
25	ExprRange	lambda_map: 30 start_index: 89 end_index: 87
26	ExprRange	lambda_map: 31 start_index: 89 end_index: 90
27	Operation	operator: 32 operand: 35
28	Operation	operator: 49 operands: 34
29	Literal
30	Lambda	parameter: 98 body: 84
31	Lambda	parameter: 98 body: 85
32	Literal
33	ExprTuple	35
34	ExprTuple	36, 37, 38
35	Lambda	parameters: 76 body: 39
36	ExprRange	lambda_map: 40 start_index: 89 end_index: 87
37	Operation	operator: 52 operands: 41
38	ExprRange	lambda_map: 42 start_index: 89 end_index: 90
39	Conditional	value: 43 condition: 44
40	Lambda	parameter: 98 body: 45
41	ExprTuple	70, 59
42	Lambda	parameter: 98 body: 46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operands: 50
45	Operation	operator: 52 operands: 51
46	Operation	operator: 52 operands: 53
47	Literal
48	ExprTuple	54, 55
49	Literal
50	ExprTuple	56, 57, 58
51	ExprTuple	84, 59
52	Literal
53	ExprTuple	85, 59
54	Operation	operator: 75 operands: 60
55	Operation	operator: 73 operands: 61
56	ExprRange	lambda_map: 62 start_index: 89 end_index: 87
57	Operation	operator: 78 operands: 63
58	ExprRange	lambda_map: 64 start_index: 89 end_index: 90
59	Operation	operator: 65 operand: 72
60	ExprTuple	81, 67, 83
61	ExprTuple	80, 68
62	Lambda	parameter: 98 body: 69
63	ExprTuple	82, 70
64	Lambda	parameter: 98 body: 71
65	Literal
66	ExprTuple	72
67	Operation	operator: 73 operands: 74
68	Operation	operator: 75 operands: 76
69	Operation	operator: 78 operands: 77
70	Variable
71	Operation	operator: 78 operands: 79
72	Variable
73	Literal
74	ExprTuple	80, 82
75	Literal
76	ExprTuple	81, 82, 83
77	ExprTuple	93, 84
78	Literal
79	ExprTuple	94, 85
80	Variable
81	ExprRange	lambda_map: 86 start_index: 89 end_index: 87
82	Variable
83	ExprRange	lambda_map: 88 start_index: 89 end_index: 90
84	IndexedVar	variable: 91 index: 98
85	IndexedVar	variable: 92 index: 98
86	Lambda	parameter: 98 body: 93
87	Variable
88	Lambda	parameter: 98 body: 94
89	Literal
90	Variable
91	Variable
92	Variable
93	IndexedVar	variable: 95 index: 98
94	IndexedVar	variable: 96 index: 98
95	Variable
96	Variable
97	ExprTuple	98
98	Variable