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
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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 27 body: 2
1	ExprTuple	27
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	27, 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Variable
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 22 operands: 19
16	Operation	operator: 22 operands: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 25
20	ExprTuple	26, 28
21	ExprTuple	24, 27, 25
22	Literal
23	ExprTuple	26, 27, 28
24	ExprRange	lambda_map: 29 start_index: 34 end_index: 32
25	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
26	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
27	Variable
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Lambda	parameter: 45 body: 36
30	Lambda	parameter: 45 body: 37
31	Lambda	parameter: 45 body: 38
32	Variable
33	Lambda	parameter: 45 body: 39
34	Literal
35	Variable
36	IndexedVar	variable: 40 index: 45
37	IndexedVar	variable: 41 index: 45
38	IndexedVar	variable: 42 index: 45
39	IndexedVar	variable: 43 index: 45
40	Variable
41	Variable
42	Variable
43	Variable
44	ExprTuple	45
45	Variable