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 A, B, C, Conditional, ExprRange, IndexedVar, K, Lambda, Variable, i, j, k
from proveit.core_expr_types import A_1_to_i, B_1_to_j, C_1_to_k
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Equals, InClass
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = VecSpaces(K)
expr = Lambda([A_1_to_i, B_1_to_j, C_1_to_k], Conditional(Equals(TensorProd(A_1_to_i, B_1_to_j, C_1_to_k), TensorProd(A_1_to_i, TensorProd(B_1_to_j), C_1_to_k)).with_wrapping_at(1), And(ExprRange(sub_expr1, InClass(IndexedVar(A, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InClass(IndexedVar(B, sub_expr1), sub_expr2), one, j), ExprRange(sub_expr1, InClass(IndexedVar(C, sub_expr1), sub_expr2), one, k))))

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(A_{1}, A_{2}, \ldots, A_{i}, B_{1}, B_{2}, \ldots, B_{j}, C_{1}, C_{2}, \ldots, C_{k}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i}{\otimes} B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}{\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \\  = \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i} {\otimes} \left(B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}\right){\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \end{array} \end{array} \textrm{ if } \left(A_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(A_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(A_{i} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(B_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(B_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(B_{j} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right), \left(C_{1} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \left(C_{2} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) ,  \ldots ,  \left(C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 13 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
8	Operation	operator: 26 operands: 13
9	Operation	operator: 26 operands: 14
10	ExprRange	lambda_map: 15 start_index: 39 end_index: 25
11	ExprRange	lambda_map: 16 start_index: 39 end_index: 40
12	ExprRange	lambda_map: 17 start_index: 39 end_index: 29
13	ExprTuple	18, 34, 20
14	ExprTuple	18, 19, 20
15	Lambda	parameter: 49 body: 21
16	Lambda	parameter: 49 body: 22
17	Lambda	parameter: 49 body: 23
18	ExprRange	lambda_map: 24 start_index: 39 end_index: 25
19	Operation	operator: 26 operands: 27
20	ExprRange	lambda_map: 28 start_index: 39 end_index: 29
21	Operation	operator: 32 operands: 30
22	Operation	operator: 32 operands: 31
23	Operation	operator: 32 operands: 33
24	Lambda	parameter: 49 body: 35
25	Variable
26	Literal
27	ExprTuple	34
28	Lambda	parameter: 49 body: 36
29	Variable
30	ExprTuple	35, 37
31	ExprTuple	45, 37
32	Literal
33	ExprTuple	36, 37
34	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
35	IndexedVar	variable: 41 index: 49
36	IndexedVar	variable: 42 index: 49
37	Operation	operator: 43 operand: 46
38	Lambda	parameter: 49 body: 45
39	Literal
40	Variable
41	Variable
42	Variable
43	Literal
44	ExprTuple	46
45	IndexedVar	variable: 47 index: 49
46	Variable
47	Variable
48	ExprTuple	49
49	Variable