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, 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 = 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\{\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..

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	25, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Variable
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 20 operands: 17
14	Operation	operator: 20 operands: 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22, 23
18	ExprTuple	24, 26
19	ExprTuple	22, 25, 23
20	Literal
21	ExprTuple	24, 25, 26
22	ExprRange	lambda_map: 27 start_index: 32 end_index: 30
23	ExprRange	lambda_map: 28 start_index: 32 end_index: 33
24	ExprRange	lambda_map: 29 start_index: 32 end_index: 30
25	Variable
26	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
27	Lambda	parameter: 43 body: 34
28	Lambda	parameter: 43 body: 35
29	Lambda	parameter: 43 body: 36
30	Variable
31	Lambda	parameter: 43 body: 37
32	Literal
33	Variable
34	IndexedVar	variable: 38 index: 43
35	IndexedVar	variable: 39 index: 43
36	IndexedVar	variable: 40 index: 43
37	IndexedVar	variable: 41 index: 43
38	Variable
39	Variable
40	Variable
41	Variable
42	ExprTuple	43
43	Variable