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, K, Lambda, 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, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [A_1_to_i, B_1_to_j, C_1_to_k], instance_expr = 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), domain = VecSpaces(K)).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural))))

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(i, j, k\right) \mapsto \left\{\begin{array}{l}\forall_{A_{1}, A_{2}, \ldots, A_{i}, B_{1}, B_{2}, \ldots, B_{j}, C_{1}, C_{2}, \ldots, C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\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}\right)\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	41, 56, 45
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 29 body: 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Conditional	value: 17 condition: 18
13	ExprTuple	41, 19
14	ExprTuple	56, 19
15	Literal
16	ExprTuple	45, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28
24	Operation	operator: 42 operands: 29
25	Operation	operator: 42 operands: 30
26	ExprRange	lambda_map: 31 start_index: 55 end_index: 41
27	ExprRange	lambda_map: 32 start_index: 55 end_index: 56
28	ExprRange	lambda_map: 33 start_index: 55 end_index: 45
29	ExprTuple	34, 50, 36
30	ExprTuple	34, 35, 36
31	Lambda	parameter: 65 body: 37
32	Lambda	parameter: 65 body: 38
33	Lambda	parameter: 65 body: 39
34	ExprRange	lambda_map: 40 start_index: 55 end_index: 41
35	Operation	operator: 42 operands: 43
36	ExprRange	lambda_map: 44 start_index: 55 end_index: 45
37	Operation	operator: 48 operands: 46
38	Operation	operator: 48 operands: 47
39	Operation	operator: 48 operands: 49
40	Lambda	parameter: 65 body: 51
41	Variable
42	Literal
43	ExprTuple	50
44	Lambda	parameter: 65 body: 52
45	Variable
46	ExprTuple	51, 53
47	ExprTuple	61, 53
48	Literal
49	ExprTuple	52, 53
50	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
51	IndexedVar	variable: 57 index: 65
52	IndexedVar	variable: 58 index: 65
53	Operation	operator: 59 operand: 62
54	Lambda	parameter: 65 body: 61
55	Literal
56	Variable
57	Variable
58	Variable
59	Literal
60	ExprTuple	62
61	IndexedVar	variable: 63 index: 65
62	Variable
63	Variable
64	ExprTuple	65
65	Variable