Expression of type Conditional

from the theory of proveit.numbers.summation

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, k, n
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, Mult, NaturalPos, Sum, frac, one, two

# build up the expression from sub-expressions
expr = Conditional(Equals(Sum(index_or_indices = [k], summand = k, domain = Interval(one, n)), frac(Mult(n, Add(n, one)), two)), InSet(n, NaturalPos))

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(\sum_{k = 1}^{n} k\right) = \frac{n \cdot \left(n + 1\right)}{2} \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 22 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	31, 8
6	Operation	operator: 9 operand: 13
7	Operation	operator: 11 operands: 12
8	Literal
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameter: 26 body: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	ExprTuple	26
17	Conditional	value: 26 condition: 20
18	Literal
19	ExprTuple	31, 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	31, 30
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Variable