Theorem number_summation_reduction of type Forall

from the theory of proveit.linear_algebra.addition

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.addition import number_summation_reduction

# check that the built expression is the same as the stored expression
assert number_summation_reduction.expr == stored_expr
assert number_summation_reduction.expr._style_id == stored_expr._style_id
print("Passed sanity check: number_summation_reduction matches stored_expr")

Passed sanity check: number_summation_reduction matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{f, Q}~\left[\forall_{n, j \in \mathbb{N}^+}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in \mathbb{C}}~\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)\right]\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 11 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	47, 48
4	Operation	operator: 11 operand: 6
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	37, 54
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 14
10	Operation	operator: 28 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	15, 16
14	Lambda	parameters: 17 body: 18
15	Operation	operator: 41 operands: 19
16	Operation	operator: 41 operands: 20
17	ExprTuple	21
18	Conditional	value: 22 condition: 23
19	ExprTuple	37, 24
20	ExprTuple	54, 24
21	ExprRange	lambda_map: 25 start_index: 53 end_index: 37
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Lambda	parameter: 58 body: 45
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Operation	operator: 33 operand: 38
31	Operation	operator: 34 operand: 38
32	ExprRange	lambda_map: 36 start_index: 53 end_index: 37
33	Literal
34	Literal
35	ExprTuple	38
36	Lambda	parameter: 58 body: 39
37	Variable
38	Lambda	parameters: 49 body: 40
39	Operation	operator: 41 operands: 42
40	Conditional	value: 43 condition: 44
41	Literal
42	ExprTuple	45, 46
43	Operation	operator: 47 operands: 49
44	Operation	operator: 48 operands: 49
45	IndexedVar	variable: 50 index: 58
46	Literal
47	Variable
48	Variable
49	ExprTuple	51
50	Variable
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