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