# from the theory of proveit.numbers.summation¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, a, fa, fx, x
from proveit.logic import Equals, InSet
from proveit.numbers import Integer, Interval, Sum

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(Equals(Sum(index_or_indices = [x], summand = fx, domain = Interval(a, a)), fa), InSet(a, Integer))))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a \mapsto \left\{\left(\sum_{x = a}^{a} f\left(x\right)\right) = f\left(a\right) \textrm{ if } a \in \mathbb{Z}\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 20
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple26, 10
8Operationoperator: 11
operand: 14
9Operationoperator: 18
operand: 26
10Literal
11Literal
12ExprTuple14
13ExprTuple26
14Lambdaparameter: 22
body: 15
15Conditionalvalue: 16
condition: 17
16Operationoperator: 18
operand: 22
17Operationoperator: 20
operands: 21
18Variable
19ExprTuple22
20Literal
21ExprTuple22, 23
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 26
26Variable