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, 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, InClass, InSet
from proveit.numbers import Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [v], instance_expr = Implies(InSet(vec_summation_b1toj_fQ, K), Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(f__b_1_to_j, v), condition = Q__b_1_to_j), ScalarMult(Sum(index_or_indices = sub_expr1, summand = f__b_1_to_j, condition = Q__b_1_to_j), v)).with_wrapping_at(1)).with_wrapping_at(2), domain = V), 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_{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[\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] \\  = \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) \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: 23 body: 3
2	ExprTuple	23
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	23, 11
10	Lambda	parameter: 45 body: 13
11	Operation	operator: 14 operand: 29
12	ExprTuple	45
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	29
16	Operation	operator: 18 operands: 19
17	Operation	operator: 24 operands: 20
18	Literal
19	ExprTuple	21, 22
20	ExprTuple	45, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Variable
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operand: 41
29	Variable
30	Operation	operator: 32 operand: 35
31	Operation	operator: 42 operands: 34
32	Literal
33	ExprTuple	35
34	ExprTuple	36, 45
35	Lambda	parameters: 50 body: 37
36	Operation	operator: 38 operand: 41
37	Conditional	value: 40 condition: 47
38	Literal
39	ExprTuple	41
40	Operation	operator: 42 operands: 43
41	Lambda	parameters: 50 body: 44
42	Literal
43	ExprTuple	46, 45
44	Conditional	value: 46 condition: 47
45	Variable
46	Operation	operator: 48 operands: 50
47	Operation	operator: 49 operands: 50
48	Variable
49	Variable
50	ExprTuple	51
51	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
52	Lambda	parameter: 58 body: 55
53	Literal
54	Variable
55	IndexedVar	variable: 56 index: 58
56	Variable
57	ExprTuple	58
58	Variable