Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 33 body: 2
1	ExprTuple	33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 24 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	33, 10
8	Operation	operator: 11 operand: 15
9	Operation	operator: 13 operands: 14
10	Literal
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 17
15	Lambda	parameter: 28 body: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	28
19	Conditional	value: 28 condition: 22
20	Literal
21	ExprTuple	33, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	33, 32
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Variable