Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

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, K, Lambda, V, j, v
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, VecSpaces, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import NaturalPos, Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ExprTuple(Lambda(j, Conditional(Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [v], instance_expr = Implies(InSet(vec_summation_b1toj_fQ, K), Equals(ScalarMult(Sum(index_or_indices = sub_expr1, summand = f__b_1_to_j, condition = Q__b_1_to_j), v), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(f__b_1_to_j, v), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2), domain = V), domain = VecSpaces(K)), InSet(j, NaturalPos))))

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(j \mapsto \left\{\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{v \in V}~\left(\begin{array}{c} \begin{array}{l} \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \in K\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \cdot v\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot v\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)\right] \textrm{ if } j \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	parameter: 62 body: 3
2	ExprTuple	62
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 32 operands: 7
6	ExprTuple	8
7	ExprTuple	62, 9
8	Lambda	parameter: 31 body: 11
9	Literal
10	ExprTuple	31
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	31, 19
18	Lambda	parameter: 55 body: 21
19	Operation	operator: 22 operand: 37
20	ExprTuple	55
21	Conditional	value: 24 condition: 25
22	Literal
23	ExprTuple	37
24	Operation	operator: 26 operands: 27
25	Operation	operator: 32 operands: 28
26	Literal
27	ExprTuple	29, 30
28	ExprTuple	55, 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Variable
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Operation	operator: 41 operand: 48
37	Variable
38	Operation	operator: 51 operands: 40
39	Operation	operator: 41 operand: 44
40	ExprTuple	43, 55
41	Literal
42	ExprTuple	44
43	Operation	operator: 45 operand: 48
44	Lambda	parameters: 58 body: 47
45	Literal
46	ExprTuple	48
47	Conditional	value: 49 condition: 53
48	Lambda	parameters: 58 body: 50
49	Operation	operator: 51 operands: 52
50	Conditional	value: 54 condition: 53
51	Literal
52	ExprTuple	54, 55
53	Operation	operator: 56 operands: 58
54	Operation	operator: 57 operands: 58
55	Variable
56	Variable
57	Variable
58	ExprTuple	59
59	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
60	Lambda	parameter: 66 body: 63
61	Literal
62	Variable
63	IndexedVar	variable: 64 index: 66
64	Variable
65	ExprTuple	66
66	Variable