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 ExprTuple, K, Lambda, Q, V, f, 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([K, f, Q], Forall(instance_param_or_params = [j], instance_expr = 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)), domain = 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(\left(K, f, Q\right) \mapsto \left[\forall_{j \in \mathbb{N}^+}~\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]\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	parameters: 2 body: 3
2	ExprTuple	41, 61, 60
3	Operation	operator: 18 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 66 body: 7
6	ExprTuple	66
7	Conditional	value: 8 condition: 9
8	Operation	operator: 18 operand: 12
9	Operation	operator: 36 operands: 11
10	ExprTuple	12
11	ExprTuple	66, 13
12	Lambda	parameter: 35 body: 15
13	Literal
14	ExprTuple	35
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	35, 23
22	Lambda	parameter: 59 body: 25
23	Operation	operator: 26 operand: 41
24	ExprTuple	59
25	Conditional	value: 28 condition: 29
26	Literal
27	ExprTuple	41
28	Operation	operator: 30 operands: 31
29	Operation	operator: 36 operands: 32
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	59, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Variable
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43
40	Operation	operator: 45 operand: 52
41	Variable
42	Operation	operator: 55 operands: 44
43	Operation	operator: 45 operand: 48
44	ExprTuple	47, 59
45	Literal
46	ExprTuple	48
47	Operation	operator: 49 operand: 52
48	Lambda	parameters: 62 body: 51
49	Literal
50	ExprTuple	52
51	Conditional	value: 53 condition: 57
52	Lambda	parameters: 62 body: 54
53	Operation	operator: 55 operands: 56
54	Conditional	value: 58 condition: 57
55	Literal
56	ExprTuple	58, 59
57	Operation	operator: 60 operands: 62
58	Operation	operator: 61 operands: 62
59	Variable
60	Variable
61	Variable
62	ExprTuple	63
63	ExprRange	lambda_map: 64 start_index: 65 end_index: 66
64	Lambda	parameter: 70 body: 67
65	Literal
66	Variable
67	IndexedVar	variable: 68 index: 70
68	Variable
69	ExprTuple	70
70	Variable