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, i, j, k
from proveit.core_expr_types import A_1_to_i, B_1_to_j, C_1_to_k
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [A_1_to_i, B_1_to_j, C_1_to_k], instance_expr = Equals(TensorProd(A_1_to_i, B_1_to_j, C_1_to_k), TensorProd(A_1_to_i, TensorProd(B_1_to_j), C_1_to_k)).with_wrapping_at(1), domain = VecSpaces(K)).with_wrapping(), domain = 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(K \mapsto \left[\forall_{i, j, k \in \mathbb{N}}~\left[\begin{array}{l}\forall_{A_{1}, A_{2}, \ldots, A_{i}, B_{1}, B_{2}, \ldots, B_{j}, C_{1}, C_{2}, \ldots, C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\left(\begin{array}{c} \begin{array}{l} \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i}{\otimes} B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}{\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \\  = \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i} {\otimes} \left(B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}\right){\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \end{array} \end{array}\right)\end{array}\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: 66 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	45, 60, 49
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 26 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14, 15
12	Lambda	parameters: 33 body: 16
13	Operation	operator: 19 operands: 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Conditional	value: 21 condition: 22
17	ExprTuple	45, 23
18	ExprTuple	60, 23
19	Literal
20	ExprTuple	49, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31, 32
28	Operation	operator: 46 operands: 33
29	Operation	operator: 46 operands: 34
30	ExprRange	lambda_map: 35 start_index: 59 end_index: 45
31	ExprRange	lambda_map: 36 start_index: 59 end_index: 60
32	ExprRange	lambda_map: 37 start_index: 59 end_index: 49
33	ExprTuple	38, 54, 40
34	ExprTuple	38, 39, 40
35	Lambda	parameter: 69 body: 41
36	Lambda	parameter: 69 body: 42
37	Lambda	parameter: 69 body: 43
38	ExprRange	lambda_map: 44 start_index: 59 end_index: 45
39	Operation	operator: 46 operands: 47
40	ExprRange	lambda_map: 48 start_index: 59 end_index: 49
41	Operation	operator: 52 operands: 50
42	Operation	operator: 52 operands: 51
43	Operation	operator: 52 operands: 53
44	Lambda	parameter: 69 body: 55
45	Variable
46	Literal
47	ExprTuple	54
48	Lambda	parameter: 69 body: 56
49	Variable
50	ExprTuple	55, 57
51	ExprTuple	65, 57
52	Literal
53	ExprTuple	56, 57
54	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
55	IndexedVar	variable: 61 index: 69
56	IndexedVar	variable: 62 index: 69
57	Operation	operator: 63 operand: 66
58	Lambda	parameter: 69 body: 65
59	Literal
60	Variable
61	Variable
62	Variable
63	Literal
64	ExprTuple	66
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable