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, ExprRange, ExprTuple, IndexedVar, K, Lambda, U, V, Variable, W, 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, InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = VecSpaces(K)
sub_expr3 = [U_1_to_i, V, W_1_to_k]
expr = ExprTuple(Lambda(sub_expr3, Conditional(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_expr3).with_wrapping(), And(ExprRange(sub_expr1, InClass(IndexedVar(U, sub_expr1), sub_expr2), one, i), InClass(V, sub_expr2), ExprRange(sub_expr1, InClass(IndexedVar(W, sub_expr1), sub_expr2), one, 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(\left(U_{1}, U_{2}, \ldots, U_{i}, V, W_{1}, W_{2}, \ldots, W_{k}\right) \mapsto \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} \textrm{ if } \left(U_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(U_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(U_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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_{k} \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, 48, 5
3	Conditional	value: 6 condition: 7
4	ExprRange	lambda_map: 8 start_index: 67 end_index: 65
5	ExprRange	lambda_map: 9 start_index: 67 end_index: 68
6	Operation	operator: 10 operand: 13
7	Operation	operator: 27 operands: 12
8	Lambda	parameter: 76 body: 62
9	Lambda	parameter: 76 body: 63
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15, 16
13	Lambda	parameters: 54 body: 17
14	ExprRange	lambda_map: 18 start_index: 67 end_index: 65
15	Operation	operator: 30 operands: 19
16	ExprRange	lambda_map: 20 start_index: 67 end_index: 68
17	Conditional	value: 21 condition: 22
18	Lambda	parameter: 76 body: 23
19	ExprTuple	48, 37
20	Lambda	parameter: 76 body: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32, 33
27	Literal
28	ExprTuple	34, 35, 36
29	ExprTuple	62, 37
30	Literal
31	ExprTuple	63, 37
32	Operation	operator: 53 operands: 38
33	Operation	operator: 51 operands: 39
34	ExprRange	lambda_map: 40 start_index: 67 end_index: 65
35	Operation	operator: 56 operands: 41
36	ExprRange	lambda_map: 42 start_index: 67 end_index: 68
37	Operation	operator: 43 operand: 50
38	ExprTuple	59, 45, 61
39	ExprTuple	58, 46
40	Lambda	parameter: 76 body: 47
41	ExprTuple	60, 48
42	Lambda	parameter: 76 body: 49
43	Literal
44	ExprTuple	50
45	Operation	operator: 51 operands: 52
46	Operation	operator: 53 operands: 54
47	Operation	operator: 56 operands: 55
48	Variable
49	Operation	operator: 56 operands: 57
50	Variable
51	Literal
52	ExprTuple	58, 60
53	Literal
54	ExprTuple	59, 60, 61
55	ExprTuple	71, 62
56	Literal
57	ExprTuple	72, 63
58	Variable
59	ExprRange	lambda_map: 64 start_index: 67 end_index: 65
60	Variable
61	ExprRange	lambda_map: 66 start_index: 67 end_index: 68
62	IndexedVar	variable: 69 index: 76
63	IndexedVar	variable: 70 index: 76
64	Lambda	parameter: 76 body: 71
65	Variable
66	Lambda	parameter: 76 body: 72
67	Literal
68	Variable
69	Variable
70	Variable
71	IndexedVar	variable: 73 index: 76
72	IndexedVar	variable: 74 index: 76
73	Variable
74	Variable
75	ExprTuple	76
76	Variable