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, ExprTuple, Function, K, Lambda, V, i, j, k, s
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, TensorProd, VecSpaces, VecSum
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Natural, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(s, sub_expr1)
sub_expr3 = ScalarMult(sub_expr2, f__b_1_to_j)
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a_1_to_i, c_1_to_k], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(a_1_to_i, sub_expr3, c_1_to_k), V), condition = Q__b_1_to_j), Equals(TensorProd(a_1_to_i, VecSum(index_or_indices = sub_expr1, summand = sub_expr3, condition = Q__b_1_to_j), c_1_to_k), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2)).with_wrapping(), domain = VecSpaces(K)).with_wrapping(), And(InSet(i, Natural), InSet(j, NaturalPos), 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}, c_{1}, c_{2}, \ldots, c_{k}}~\\
\left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right)\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	75, 86, 79
3	Conditional	value: 4 condition: 5
4	Operation	operator: 36 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameter: 55 body: 14
10	Operation	operator: 49 operands: 15
11	Operation	operator: 49 operands: 16
12	Operation	operator: 49 operands: 17
13	ExprTuple	55
14	Conditional	value: 18 condition: 19
15	ExprTuple	75, 21
16	ExprTuple	86, 20
17	ExprTuple	79, 21
18	Operation	operator: 36 operand: 25
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	55, 26
25	Lambda	parameters: 27 body: 28
26	Operation	operator: 29 operand: 33
27	ExprTuple	70, 72
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Operation	operator: 36 operand: 40
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40
38	Literal
39	ExprTuple	41, 42
40	Lambda	parameters: 77 body: 43
41	Operation	operator: 67 operands: 44
42	Operation	operator: 51 operand: 48
43	Conditional	value: 46 condition: 62
44	ExprTuple	70, 47, 72
45	ExprTuple	48
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operand: 56
48	Lambda	parameters: 77 body: 53
49	Literal
50	ExprTuple	54, 55
51	Literal
52	ExprTuple	56
53	Conditional	value: 57 condition: 62
54	Operation	operator: 67 operands: 58
55	Variable
56	Lambda	parameters: 77 body: 59
57	Operation	operator: 64 operands: 60
58	ExprTuple	70, 61, 72
59	Conditional	value: 61 condition: 62
60	ExprTuple	69, 63
61	Operation	operator: 64 operands: 65
62	Operation	operator: 66 operands: 77
63	Operation	operator: 67 operands: 68
64	Literal
65	ExprTuple	69, 71
66	Variable
67	Literal
68	ExprTuple	70, 71, 72
69	Operation	operator: 73 operands: 77
70	ExprRange	lambda_map: 74 start_index: 85 end_index: 75
71	Operation	operator: 76 operands: 77
72	ExprRange	lambda_map: 78 start_index: 85 end_index: 79
73	Variable
74	Lambda	parameter: 91 body: 80
75	Variable
76	Variable
77	ExprTuple	81
78	Lambda	parameter: 91 body: 82
79	Variable
80	IndexedVar	variable: 83 index: 91
81	ExprRange	lambda_map: 84 start_index: 85 end_index: 86
82	IndexedVar	variable: 87 index: 91
83	Variable
84	Lambda	parameter: 91 body: 88
85	Literal
86	Variable
87	Variable
88	IndexedVar	variable: 89 index: 91
89	Variable
90	ExprTuple	91
91	Variable