Theorem summation_nat_closure of type Forall

from the theory of proveit.numbers.summation

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.numbers.summation import summation_nat_closure

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

Passed sanity check: summation_nat_closure matches stored_expr

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

\forall_{f, Q}~\left(\left[\forall_{x~|~Q\left(x\right)}~\left(f\left(x\right) \in \mathbb{N}\right)\right] \Rightarrow \left(\left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \mathbb{N}\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: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	25, 26
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 19 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 22
12	Lambda	parameter: 28 body: 14
13	Operation	operator: 15 operand: 18
14	Conditional	value: 17 condition: 24
15	Literal
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	Lambda	parameter: 28 body: 21
19	Literal
20	ExprTuple	23, 22
21	Conditional	value: 23 condition: 24
22	Literal
23	Operation	operator: 25 operand: 28
24	Operation	operator: 26 operand: 28
25	Variable
26	Variable
27	ExprTuple	28
28	Variable