Theorem sum_first_n_int 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 sum_first_n_int

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

Passed sanity check: sum_first_n_int matches stored_expr

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

\forall_{n \in \mathbb{N}^+}~\left(\left(\sum_{k = 1}^{n} k\right) = \frac{n \cdot \left(n + 1\right)}{2}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 36 body: 5
4	ExprTuple	36
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 27 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	36, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 20
18	Lambda	parameter: 31 body: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	ExprTuple	31
22	Conditional	value: 31 condition: 25
23	Literal
24	ExprTuple	36, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	36, 35
31	Variable
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Variable