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, 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 Equals, Forall, Implies, InClass, InSet

# 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(V, Conditional(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(), InClass(V, VecSpaces(K)))))

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