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, e
from proveit.core_expr_types import a_1_to_i, c_1_to_k, d_1_to_i, f_1_to_k
from proveit.linear_algebra import TensorProd, VecZero
from proveit.logic import And, Equals, Implies, InSet, NotEquals

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([b, e], Conditional(Implies(Equals(TensorProd(a_1_to_i, b, c_1_to_k), TensorProd(d_1_to_i, e, f_1_to_k)).with_wrapping_at(2), Equals(TensorProd(a_1_to_i, c_1_to_k), TensorProd(d_1_to_i, f_1_to_k)).with_wrapping_at(2)).with_wrapping_at(2), And(InSet(b, V), InSet(e, V), Equals(b, e), NotEquals(b, VecZero(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(\left(b, e\right) \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} 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} e{\otimes} f_{1} {\otimes}  f_{2} {\otimes}  \ldots {\otimes}  f_{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} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(d_{1} {\otimes}  d_{2} {\otimes}  \ldots {\otimes}  d_{i}{\otimes} f_{1} {\otimes}  f_{2} {\otimes}  \ldots {\otimes}  f_{k}\right) \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } b \in V ,  e \in V ,  b = e ,  b \neq \vec{0}\left(V\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: 21 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, 14
9	Operation	operator: 20 operands: 15
10	Operation	operator: 20 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 22 operands: 23
15	ExprTuple	24, 25
16	ExprTuple	26, 27
17	ExprTuple	36, 42
18	Literal
19	ExprTuple	37, 42
20	Literal
21	ExprTuple	36, 37
22	Literal
23	ExprTuple	36, 28
24	Operation	operator: 32 operands: 29
25	Operation	operator: 32 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operand: 42
29	ExprTuple	38, 36, 39
30	ExprTuple	40, 37, 41
31	ExprTuple	38, 39
32	Literal
33	ExprTuple	40, 41
34	Literal
35	ExprTuple	42
36	Variable
37	Variable
38	ExprRange	lambda_map: 43 start_index: 48 end_index: 46
39	ExprRange	lambda_map: 44 start_index: 48 end_index: 49
40	ExprRange	lambda_map: 45 start_index: 48 end_index: 46
41	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
42	Variable
43	Lambda	parameter: 59 body: 50
44	Lambda	parameter: 59 body: 51
45	Lambda	parameter: 59 body: 52
46	Variable
47	Lambda	parameter: 59 body: 53
48	Literal
49	Variable
50	IndexedVar	variable: 54 index: 59
51	IndexedVar	variable: 55 index: 59
52	IndexedVar	variable: 56 index: 59
53	IndexedVar	variable: 57 index: 59
54	Variable
55	Variable
56	Variable
57	Variable
58	ExprTuple	59
59	Variable