Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 20 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 19 operands: 14
9	Operation	operator: 19 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 19 operands: 20
13	Operation	operator: 21 operands: 22
14	ExprTuple	23, 24
15	ExprTuple	25, 26
16	ExprTuple	35, 41
17	Literal
18	ExprTuple	36, 41
19	Literal
20	ExprTuple	35, 36
21	Literal
22	ExprTuple	35, 27
23	Operation	operator: 31 operands: 28
24	Operation	operator: 31 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operand: 41
28	ExprTuple	37, 35, 38
29	ExprTuple	39, 36, 40
30	ExprTuple	37, 38
31	Literal
32	ExprTuple	39, 40
33	Literal
34	ExprTuple	41
35	Variable
36	Variable
37	ExprRange	lambda_map: 42 start_index: 47 end_index: 45
38	ExprRange	lambda_map: 43 start_index: 47 end_index: 48
39	ExprRange	lambda_map: 44 start_index: 47 end_index: 45
40	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
41	Variable
42	Lambda	parameter: 58 body: 49
43	Lambda	parameter: 58 body: 50
44	Lambda	parameter: 58 body: 51
45	Variable
46	Lambda	parameter: 58 body: 52
47	Literal
48	Variable
49	IndexedVar	variable: 53 index: 58
50	IndexedVar	variable: 54 index: 58
51	IndexedVar	variable: 55 index: 58
52	IndexedVar	variable: 56 index: 58
53	Variable
54	Variable
55	Variable
56	Variable
57	ExprTuple	58
58	Variable