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, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Implies, InSet
from proveit.numbers import Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ExprTuple(Lambda(v, Conditional(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), InSet(v, V))))

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\{\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} \textrm{ if } v \in V\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: 33 body: 3
2	ExprTuple	33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 12 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	33, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Variable
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 20 operand: 29
17	Variable
18	Operation	operator: 20 operand: 23
19	Operation	operator: 30 operands: 22
20	Literal
21	ExprTuple	23
22	ExprTuple	24, 33
23	Lambda	parameters: 38 body: 25
24	Operation	operator: 26 operand: 29
25	Conditional	value: 28 condition: 35
26	Literal
27	ExprTuple	29
28	Operation	operator: 30 operands: 31
29	Lambda	parameters: 38 body: 32
30	Literal
31	ExprTuple	34, 33
32	Conditional	value: 34 condition: 35
33	Variable
34	Operation	operator: 36 operands: 38
35	Operation	operator: 37 operands: 38
36	Variable
37	Variable
38	ExprTuple	39
39	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
40	Lambda	parameter: 46 body: 43
41	Literal
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable