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, 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, InClass, InSet
from proveit.numbers import Mult

# 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(V, Conditional(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), 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\{\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) \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: 28 body: 3
2	ExprTuple	28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	28, 11
10	Lambda	parameter: 51 body: 13
11	Operation	operator: 14 operand: 23
12	ExprTuple	51
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	23
16	Operation	operator: 18 operands: 19
17	Operation	operator: 24 operands: 20
18	Literal
19	ExprTuple	21, 22
20	ExprTuple	51, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	ExprTuple	33, 28
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Operation	operator: 45 operands: 31
30	Operation	operator: 35 operand: 34
31	ExprTuple	51, 33
32	ExprTuple	34
33	Operation	operator: 35 operand: 38
34	Lambda	parameters: 55 body: 37
35	Literal
36	ExprTuple	38
37	Conditional	value: 39 condition: 43
38	Lambda	parameters: 55 body: 40
39	Operation	operator: 45 operands: 41
40	Conditional	value: 42 condition: 43
41	ExprTuple	44, 50
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 55
44	Operation	operator: 48 operands: 49
45	Literal
46	ExprTuple	52, 50
47	Variable
48	Literal
49	ExprTuple	51, 52
50	Operation	operator: 53 operands: 55
51	Variable
52	Operation	operator: 54 operands: 55
53	Variable
54	Variable
55	ExprTuple	56
56	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
57	Lambda	parameter: 63 body: 60
58	Literal
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable