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, Lambda, 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 = ExprTuple(Lambda([a_1_to_i, b_1_to_j, c_1_to_k], 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, 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(\left(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \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} \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..\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: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operands: 14
10	Operation	operator: 25 operands: 15
11	ExprRange	lambda_map: 16 start_index: 42 end_index: 28
12	ExprRange	lambda_map: 17 start_index: 42 end_index: 43
13	ExprRange	lambda_map: 18 start_index: 42 end_index: 30
14	ExprTuple	20, 19, 21
15	ExprTuple	20, 35, 21
16	Lambda	parameter: 52 body: 22
17	Lambda	parameter: 52 body: 23
18	Lambda	parameter: 52 body: 24
19	Operation	operator: 25 operands: 26
20	ExprRange	lambda_map: 27 start_index: 42 end_index: 28
21	ExprRange	lambda_map: 29 start_index: 42 end_index: 30
22	Operation	operator: 33 operands: 31
23	Operation	operator: 33 operands: 32
24	Operation	operator: 33 operands: 34
25	Literal
26	ExprTuple	35
27	Lambda	parameter: 52 body: 36
28	Variable
29	Lambda	parameter: 52 body: 39
30	Variable
31	ExprTuple	36, 37
32	ExprTuple	49, 38
33	Literal
34	ExprTuple	39, 40
35	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
36	IndexedVar	variable: 44 index: 52
37	IndexedVar	variable: 45 index: 52
38	IndexedVar	variable: 46 index: 52
39	IndexedVar	variable: 47 index: 52
40	IndexedVar	variable: 48 index: 52
41	Lambda	parameter: 52 body: 49
42	Literal
43	Variable
44	Variable
45	Variable
46	Variable
47	Variable
48	Variable
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable