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, Function, K, Lambda, Q, V, c, f, j, k
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.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Mult, NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(c, sub_expr1)
sub_expr3 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, f__b_1_to_j), condition = Q__b_1_to_j)
expr = ExprTuple(Lambda([K, f, Q, c], Forall(instance_param_or_params = [j], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [k], instance_expr = Implies(InSet(sub_expr3, V), Equals(ScalarMult(k, sub_expr3), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(k, sub_expr2), f__b_1_to_j), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(1), domain = K), 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, c\right) \mapsto \left[\forall_{j \in \mathbb{N}^+}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{k \in K}~\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)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \in V\right) \\  \Rightarrow \left(\begin{array}{c} \begin{array}{l} \left(k \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(k \cdot c\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\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	35, 65, 59, 66
3	Operation	operator: 18 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 71 body: 7
6	ExprTuple	71
7	Conditional	value: 8 condition: 9
8	Operation	operator: 18 operand: 12
9	Operation	operator: 36 operands: 11
10	ExprTuple	12
11	ExprTuple	71, 13
12	Lambda	parameter: 40 body: 15
13	Literal
14	ExprTuple	40
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	40, 23
22	Lambda	parameter: 63 body: 25
23	Operation	operator: 26 operand: 35
24	ExprTuple	63
25	Conditional	value: 28 condition: 29
26	Literal
27	ExprTuple	35
28	Operation	operator: 30 operands: 31
29	Operation	operator: 36 operands: 32
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	63, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Variable
36	Literal
37	ExprTuple	45, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Operation	operator: 57 operands: 43
42	Operation	operator: 47 operand: 46
43	ExprTuple	63, 45
44	ExprTuple	46
45	Operation	operator: 47 operand: 50
46	Lambda	parameters: 67 body: 49
47	Literal
48	ExprTuple	50
49	Conditional	value: 51 condition: 55
50	Lambda	parameters: 67 body: 52
51	Operation	operator: 57 operands: 53
52	Conditional	value: 54 condition: 55
53	ExprTuple	56, 62
54	Operation	operator: 57 operands: 58
55	Operation	operator: 59 operands: 67
56	Operation	operator: 60 operands: 61
57	Literal
58	ExprTuple	64, 62
59	Variable
60	Literal
61	ExprTuple	63, 64
62	Operation	operator: 65 operands: 67
63	Variable
64	Operation	operator: 66 operands: 67
65	Variable
66	Variable
67	ExprTuple	68
68	ExprRange	lambda_map: 69 start_index: 70 end_index: 71
69	Lambda	parameter: 75 body: 72
70	Literal
71	Variable
72	IndexedVar	variable: 73 index: 75
73	Variable
74	ExprTuple	75
75	Variable