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 Conditional, 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 And, 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([i, j, k], Conditional(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(VecAdd(ExprRange(sub_expr1, TensorProd(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j)), sub_expr2).with_wrapping_at(2)).with_wrapping_at(2)).with_wrapping(), 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(\left(i, j, k\right) \mapsto \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(\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) =  \\ \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) \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array}\right]\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\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	parameters: 2 body: 3
2	ExprTuple	61, 55, 65
3	Conditional	value: 4 condition: 5
4	Operation	operator: 21 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 40 body: 14
10	Operation	operator: 36 operands: 15
11	Operation	operator: 36 operands: 16
12	Operation	operator: 36 operands: 17
13	ExprTuple	40
14	Conditional	value: 18 condition: 19
15	ExprTuple	61, 20
16	ExprTuple	55, 20
17	ExprTuple	65, 20
18	Operation	operator: 21 operand: 25
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	40, 26
25	Lambda	parameters: 27 body: 28
26	Operation	operator: 29 operand: 33
27	ExprTuple	56, 51, 58
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	42, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Operation	operator: 48 operands: 43
42	Operation	operator: 52 operands: 44
43	ExprTuple	45
44	ExprTuple	56, 46, 58
45	ExprRange	lambda_map: 47 start_index: 64 end_index: 55
46	Operation	operator: 48 operands: 49
47	Lambda	parameter: 68 body: 50
48	Literal
49	ExprTuple	51
50	Operation	operator: 52 operands: 53
51	ExprRange	lambda_map: 54 start_index: 64 end_index: 55
52	Literal
53	ExprTuple	56, 57, 58
54	Lambda	parameter: 73 body: 59
55	Variable
56	ExprRange	lambda_map: 60 start_index: 64 end_index: 61
57	IndexedVar	variable: 66 index: 68
58	ExprRange	lambda_map: 63 start_index: 64 end_index: 65
59	IndexedVar	variable: 66 index: 73
60	Lambda	parameter: 73 body: 67
61	Variable
62	ExprTuple	68
63	Lambda	parameter: 73 body: 69
64	Literal
65	Variable
66	Variable
67	IndexedVar	variable: 70 index: 73
68	Variable
69	IndexedVar	variable: 71 index: 73
70	Variable
71	Variable
72	ExprTuple	73
73	Variable