Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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, Lambda, Q, f
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Complex
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, Q], Implies(Forall(instance_param_or_params = [b_1_to_j], instance_expr = InSet(f__b_1_to_j, Complex), condition = Q__b_1_to_j), Equals(vec_summation_b1toj_fQ, summation_b1toj_fQ)).with_wrapping_at(2)))

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(f, Q\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\forall_{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) \in \mathbb{C}\right)\right] \Rightarrow  \\ \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] = \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]\right) \end{array} \end{array}\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	27, 28
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameters: 29 body: 15
13	Operation	operator: 16 operand: 20
14	Operation	operator: 17 operand: 20
15	Conditional	value: 19 condition: 26
16	Literal
17	Literal
18	ExprTuple	20
19	Operation	operator: 21 operands: 22
20	Lambda	parameters: 29 body: 23
21	Literal
22	ExprTuple	25, 24
23	Conditional	value: 25 condition: 26
24	Literal
25	Operation	operator: 27 operands: 29
26	Operation	operator: 28 operands: 29
27	Variable
28	Variable
29	ExprTuple	30
30	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
31	Lambda	parameter: 37 body: 34
32	Literal
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable