Expression of type ExprTuple

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 ExprRange, ExprTuple, IndexedVar, K, Lambda, V, Variable, b, 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, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = TensorProd(a_1_to_i, VecAdd(b_1_to_j), c_1_to_k)
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Implies(InSet(sub_expr2, V), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, TensorProd(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2)).with_wrapping_at(2)).with_wrapping(), 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())

\left(K \mapsto \left[\forall_{i, j, k \in \mathbb{N}}~\left[\begin{array}{l}\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\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}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{1}{\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_{2}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) +  \ldots +  \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b_{j}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right) \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array}\right]\end{array}\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 36 body: 2
2	Operation	operator: 24 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	64, 56, 69
6	Conditional	value: 7 condition: 8
7	Operation	operator: 24 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14, 15
12	Lambda	parameter: 43 body: 17
13	Operation	operator: 39 operands: 18
14	Operation	operator: 39 operands: 19
15	Operation	operator: 39 operands: 20
16	ExprTuple	43
17	Conditional	value: 21 condition: 22
18	ExprTuple	64, 23
19	ExprTuple	56, 23
20	ExprTuple	69, 23
21	Operation	operator: 24 operand: 28
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	43, 29
28	Lambda	parameters: 30 body: 31
29	Operation	operator: 32 operand: 36
30	ExprTuple	60, 53, 62
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operands: 42
39	Literal
40	ExprTuple	44, 43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Operation	operator: 57 operands: 46
45	Operation	operator: 50 operands: 47
46	ExprTuple	60, 48, 62
47	ExprTuple	49
48	Operation	operator: 50 operands: 51
49	ExprRange	lambda_map: 52 start_index: 68 end_index: 56
50	Literal
51	ExprTuple	53
52	Lambda	parameter: 71 body: 54
53	ExprRange	lambda_map: 55 start_index: 68 end_index: 56
54	Operation	operator: 57 operands: 58
55	Lambda	parameter: 76 body: 59
56	Variable
57	Literal
58	ExprTuple	60, 61, 62
59	IndexedVar	variable: 65 index: 76
60	ExprRange	lambda_map: 63 start_index: 68 end_index: 64
61	IndexedVar	variable: 65 index: 71
62	ExprRange	lambda_map: 67 start_index: 68 end_index: 69
63	Lambda	parameter: 76 body: 70
64	Variable
65	Variable
66	ExprTuple	71
67	Lambda	parameter: 76 body: 72
68	Literal
69	Variable
70	IndexedVar	variable: 73 index: 76
71	Variable
72	IndexedVar	variable: 74 index: 76
73	Variable
74	Variable
75	ExprTuple	76
76	Variable