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 ExprRange, ExprTuple, IndexedVar, Lambda, V, Variable, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.linear_algebra import TensorProd, VecAdd
from proveit.logic import Equals, Implies, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = TensorProd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Implies(InSet(sub_expr2, V), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, TensorProd(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2)).with_wrapping_at(2)))

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(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{1}{\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_{2}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) +  \ldots +  \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{j}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right) \end{array} \end{array}\right) \end{array} \end{array}\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: 2 body: 3
2	ExprTuple	29, 22, 31
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	13, 12
10	Literal
11	ExprTuple	13, 14
12	Variable
13	Operation	operator: 26 operands: 15
14	Operation	operator: 19 operands: 16
15	ExprTuple	29, 17, 31
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	ExprRange	lambda_map: 21 start_index: 37 end_index: 25
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 40 body: 23
22	ExprRange	lambda_map: 24 start_index: 37 end_index: 25
23	Operation	operator: 26 operands: 27
24	Lambda	parameter: 45 body: 28
25	Variable
26	Literal
27	ExprTuple	29, 30, 31
28	IndexedVar	variable: 34 index: 45
29	ExprRange	lambda_map: 32 start_index: 37 end_index: 33
30	IndexedVar	variable: 34 index: 40
31	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
32	Lambda	parameter: 45 body: 39
33	Variable
34	Variable
35	ExprTuple	40
36	Lambda	parameter: 45 body: 41
37	Literal
38	Variable
39	IndexedVar	variable: 42 index: 45
40	Variable
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable