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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, 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 = 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\{\left(\sum_{x = a}^{a} f\left(x\right)\right) = f\left(a\right) \textrm{ if } a \in \mathbb{Z}\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 18
operands: 5
3Literal
4ExprTuple6, 7
5ExprTuple24, 8
6Operationoperator: 9
operand: 12
7Operationoperator: 16
operand: 24
8Literal
9Literal
10ExprTuple12
11ExprTuple24
12Lambdaparameter: 20
body: 13
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operand: 20
15Operationoperator: 18
operands: 19
16Variable
17ExprTuple20
18Literal
19ExprTuple20, 21
20Variable
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 24
24Variable