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 A, B, C, Conditional, ExprRange, IndexedVar, K, Variable, 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, 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)
expr = Conditional(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), And(ExprRange(sub_expr1, InClass(IndexedVar(A, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InClass(IndexedVar(B, sub_expr1), sub_expr2), one, j), ExprRange(sub_expr1, InClass(IndexedVar(C, 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\{\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} \textrm{ if } \left(A_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(A_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(A_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(B_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(B_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(B_{j} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(C_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(C_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 23 operands: 12
8	Operation	operator: 23 operands: 13
9	ExprRange	lambda_map: 14 start_index: 38 end_index: 26
10	ExprRange	lambda_map: 15 start_index: 38 end_index: 39
11	ExprRange	lambda_map: 16 start_index: 38 end_index: 28
12	ExprTuple	18, 17, 19
13	ExprTuple	18, 33, 19
14	Lambda	parameter: 48 body: 20
15	Lambda	parameter: 48 body: 21
16	Lambda	parameter: 48 body: 22
17	Operation	operator: 23 operands: 24
18	ExprRange	lambda_map: 25 start_index: 38 end_index: 26
19	ExprRange	lambda_map: 27 start_index: 38 end_index: 28
20	Operation	operator: 31 operands: 29
21	Operation	operator: 31 operands: 30
22	Operation	operator: 31 operands: 32
23	Literal
24	ExprTuple	33
25	Lambda	parameter: 48 body: 34
26	Variable
27	Lambda	parameter: 48 body: 35
28	Variable
29	ExprTuple	34, 36
30	ExprTuple	44, 36
31	Literal
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	IndexedVar	variable: 40 index: 48
35	IndexedVar	variable: 41 index: 48
36	Operation	operator: 42 operand: 45
37	Lambda	parameter: 48 body: 44
38	Literal
39	Variable
40	Variable
41	Variable
42	Literal
43	ExprTuple	45
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable