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, ExprRange, IndexedVar, Lambda, U, V, Variable, W, a, b, c, 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
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Conditional(Equals(TensorProd(a_1_to_i, TensorProd(b_1_to_j), c_1_to_k), TensorProd(a_1_to_i, b_1_to_j, c_1_to_k)).with_wrapping_at(1), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), IndexedVar(U, sub_expr1)), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), IndexedVar(V, sub_expr1)), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), IndexedVar(W, sub_expr1)), 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} \left(b_{1} {\otimes}  b_{2} {\otimes}  \ldots {\otimes}  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \\  = \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) \end{array} \end{array} \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right), \left(b_{1} \in V_{1}\right) ,  \left(b_{2} \in V_{2}\right) ,  \ldots ,  \left(b_{j} \in V_{j}\right), \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\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: 14 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: 24 operands: 13
9	Operation	operator: 24 operands: 14
10	ExprRange	lambda_map: 15 start_index: 41 end_index: 27
11	ExprRange	lambda_map: 16 start_index: 41 end_index: 42
12	ExprRange	lambda_map: 17 start_index: 41 end_index: 29
13	ExprTuple	19, 18, 20
14	ExprTuple	19, 34, 20
15	Lambda	parameter: 51 body: 21
16	Lambda	parameter: 51 body: 22
17	Lambda	parameter: 51 body: 23
18	Operation	operator: 24 operands: 25
19	ExprRange	lambda_map: 26 start_index: 41 end_index: 27
20	ExprRange	lambda_map: 28 start_index: 41 end_index: 29
21	Operation	operator: 32 operands: 30
22	Operation	operator: 32 operands: 31
23	Operation	operator: 32 operands: 33
24	Literal
25	ExprTuple	34
26	Lambda	parameter: 51 body: 35
27	Variable
28	Lambda	parameter: 51 body: 38
29	Variable
30	ExprTuple	35, 36
31	ExprTuple	48, 37
32	Literal
33	ExprTuple	38, 39
34	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
35	IndexedVar	variable: 43 index: 51
36	IndexedVar	variable: 44 index: 51
37	IndexedVar	variable: 45 index: 51
38	IndexedVar	variable: 46 index: 51
39	IndexedVar	variable: 47 index: 51
40	Lambda	parameter: 51 body: 48
41	Literal
42	Variable
43	Variable
44	Variable
45	Variable
46	Variable
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable