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, ExprTuple, Lambda, V, b
from proveit.core_expr_types import a_1_to_i, c_1_to_k, d_1_to_i, e_1_to_k
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Implies, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(b, Conditional(Implies(Equals(TensorProd(a_1_to_i, c_1_to_k), TensorProd(d_1_to_i, e_1_to_k)).with_wrapping_at(2), Equals(TensorProd(a_1_to_i, b, c_1_to_k), TensorProd(d_1_to_i, b, e_1_to_k)).with_wrapping_at(2)).with_wrapping_at(2), InSet(b, V))))

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(b \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(d_{1} {\otimes}  d_{2} {\otimes}  \ldots {\otimes}  d_{i}{\otimes} e_{1} {\otimes}  e_{2} {\otimes}  \ldots {\otimes}  e_{k}\right) \end{array} \end{array}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(d_{1} {\otimes}  d_{2} {\otimes}  \ldots {\otimes}  d_{i} {\otimes} b{\otimes} e_{1} {\otimes}  e_{2} {\otimes}  \ldots {\otimes}  e_{k}\right) \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } b \in V\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	parameter: 28 body: 3
2	ExprTuple	28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	28, 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Variable
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 23 operands: 20
17	Operation	operator: 23 operands: 21
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 26
21	ExprTuple	27, 29
22	ExprTuple	25, 28, 26
23	Literal
24	ExprTuple	27, 28, 29
25	ExprRange	lambda_map: 30 start_index: 35 end_index: 33
26	ExprRange	lambda_map: 31 start_index: 35 end_index: 36
27	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
28	Variable
29	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
30	Lambda	parameter: 46 body: 37
31	Lambda	parameter: 46 body: 38
32	Lambda	parameter: 46 body: 39
33	Variable
34	Lambda	parameter: 46 body: 40
35	Literal
36	Variable
37	IndexedVar	variable: 41 index: 46
38	IndexedVar	variable: 42 index: 46
39	IndexedVar	variable: 43 index: 46
40	IndexedVar	variable: 44 index: 46
41	Variable
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable