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, ExprRange, IndexedVar, U, V, Variable, W, a, b, c, 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
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(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(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), IndexedVar(V, sub_expr1)), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), 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} 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} \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right), \left(b_{1} \in V_{1}\right) ,  \left(b_{2} \in V_{2}\right) ,  \ldots ,  \left(b_{j} \in V_{j}\right), \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\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: 25 operands: 12
8	Operation	operator: 25 operands: 13
9	ExprRange	lambda_map: 14 start_index: 40 end_index: 24
10	ExprRange	lambda_map: 15 start_index: 40 end_index: 41
11	ExprRange	lambda_map: 16 start_index: 40 end_index: 28
12	ExprTuple	17, 33, 19
13	ExprTuple	17, 18, 19
14	Lambda	parameter: 50 body: 20
15	Lambda	parameter: 50 body: 21
16	Lambda	parameter: 50 body: 22
17	ExprRange	lambda_map: 23 start_index: 40 end_index: 24
18	Operation	operator: 25 operands: 26
19	ExprRange	lambda_map: 27 start_index: 40 end_index: 28
20	Operation	operator: 31 operands: 29
21	Operation	operator: 31 operands: 30
22	Operation	operator: 31 operands: 32
23	Lambda	parameter: 50 body: 34
24	Variable
25	Literal
26	ExprTuple	33
27	Lambda	parameter: 50 body: 37
28	Variable
29	ExprTuple	34, 35
30	ExprTuple	47, 36
31	Literal
32	ExprTuple	37, 38
33	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
34	IndexedVar	variable: 42 index: 50
35	IndexedVar	variable: 43 index: 50
36	IndexedVar	variable: 44 index: 50
37	IndexedVar	variable: 45 index: 50
38	IndexedVar	variable: 46 index: 50
39	Lambda	parameter: 50 body: 47
40	Literal
41	Variable
42	Variable
43	Variable
44	Variable
45	Variable
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable