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 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 Equals, Forall
from proveit.numbers import Natural

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

K \mapsto \left[\forall_{i, j, k \in \mathbb{N}}~\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} \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}\right)\end{array}\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 65 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	46, 59, 48
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 25 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13, 14
11	Lambda	parameters: 33 body: 15
12	Operation	operator: 18 operands: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Conditional	value: 20 condition: 21
16	ExprTuple	46, 22
17	ExprTuple	59, 22
18	Literal
19	ExprTuple	48, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30, 31
27	Operation	operator: 43 operands: 32
28	Operation	operator: 43 operands: 33
29	ExprRange	lambda_map: 34 start_index: 58 end_index: 46
30	ExprRange	lambda_map: 35 start_index: 58 end_index: 59
31	ExprRange	lambda_map: 36 start_index: 58 end_index: 48
32	ExprTuple	38, 37, 39
33	ExprTuple	38, 53, 39
34	Lambda	parameter: 68 body: 40
35	Lambda	parameter: 68 body: 41
36	Lambda	parameter: 68 body: 42
37	Operation	operator: 43 operands: 44
38	ExprRange	lambda_map: 45 start_index: 58 end_index: 46
39	ExprRange	lambda_map: 47 start_index: 58 end_index: 48
40	Operation	operator: 51 operands: 49
41	Operation	operator: 51 operands: 50
42	Operation	operator: 51 operands: 52
43	Literal
44	ExprTuple	53
45	Lambda	parameter: 68 body: 54
46	Variable
47	Lambda	parameter: 68 body: 55
48	Variable
49	ExprTuple	54, 56
50	ExprTuple	64, 56
51	Literal
52	ExprTuple	55, 56
53	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
54	IndexedVar	variable: 60 index: 68
55	IndexedVar	variable: 61 index: 68
56	Operation	operator: 62 operand: 65
57	Lambda	parameter: 68 body: 64
58	Literal
59	Variable
60	Variable
61	Variable
62	Literal
63	ExprTuple	65
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable