Expression of type ExprTuple

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