Expression of type Conditional

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, K, 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 And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(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, TensorProd(B_1_to_j), C_1_to_k), TensorProd(A_1_to_i, B_1_to_j, C_1_to_k)).with_wrapping_at(1), domain = VecSpaces(K)).with_wrapping(), And(InSet(i, Natural), InSet(j, 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\{\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} \left(B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}\right){\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \\  = \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) \end{array} \end{array}\right)\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 28 body: 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Conditional	value: 15 condition: 16
11	ExprTuple	41, 17
12	ExprTuple	54, 17
13	Literal
14	ExprTuple	43, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 38 operands: 27
23	Operation	operator: 38 operands: 28
24	ExprRange	lambda_map: 29 start_index: 53 end_index: 41
25	ExprRange	lambda_map: 30 start_index: 53 end_index: 54
26	ExprRange	lambda_map: 31 start_index: 53 end_index: 43
27	ExprTuple	33, 32, 34
28	ExprTuple	33, 48, 34
29	Lambda	parameter: 63 body: 35
30	Lambda	parameter: 63 body: 36
31	Lambda	parameter: 63 body: 37
32	Operation	operator: 38 operands: 39
33	ExprRange	lambda_map: 40 start_index: 53 end_index: 41
34	ExprRange	lambda_map: 42 start_index: 53 end_index: 43
35	Operation	operator: 46 operands: 44
36	Operation	operator: 46 operands: 45
37	Operation	operator: 46 operands: 47
38	Literal
39	ExprTuple	48
40	Lambda	parameter: 63 body: 49
41	Variable
42	Lambda	parameter: 63 body: 50
43	Variable
44	ExprTuple	49, 51
45	ExprTuple	59, 51
46	Literal
47	ExprTuple	50, 51
48	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
49	IndexedVar	variable: 55 index: 63
50	IndexedVar	variable: 56 index: 63
51	Operation	operator: 57 operand: 60
52	Lambda	parameter: 63 body: 59
53	Literal
54	Variable
55	Variable
56	Variable
57	Literal
58	ExprTuple	60
59	IndexedVar	variable: 61 index: 63
60	Variable
61	Variable
62	ExprTuple	63
63	Variable