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, 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 = 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\{\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..

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	9, 10, 11, 12
7	Operation	operator: 18 operands: 13
8	Operation	operator: 18 operands: 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 20 operands: 21
13	ExprTuple	22, 23
14	ExprTuple	24, 25
15	ExprTuple	34, 40
16	Literal
17	ExprTuple	35, 40
18	Literal
19	ExprTuple	34, 35
20	Literal
21	ExprTuple	34, 26
22	Operation	operator: 30 operands: 27
23	Operation	operator: 30 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Operation	operator: 32 operand: 40
27	ExprTuple	36, 34, 37
28	ExprTuple	38, 35, 39
29	ExprTuple	36, 37
30	Literal
31	ExprTuple	38, 39
32	Literal
33	ExprTuple	40
34	Variable
35	Variable
36	ExprRange	lambda_map: 41 start_index: 46 end_index: 44
37	ExprRange	lambda_map: 42 start_index: 46 end_index: 47
38	ExprRange	lambda_map: 43 start_index: 46 end_index: 44
39	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
40	Variable
41	Lambda	parameter: 57 body: 48
42	Lambda	parameter: 57 body: 49
43	Lambda	parameter: 57 body: 50
44	Variable
45	Lambda	parameter: 57 body: 51
46	Literal
47	Variable
48	IndexedVar	variable: 52 index: 57
49	IndexedVar	variable: 53 index: 57
50	IndexedVar	variable: 54 index: 57
51	IndexedVar	variable: 55 index: 57
52	Variable
53	Variable
54	Variable
55	Variable
56	ExprTuple	57
57	Variable