# 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 a, f, fa, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Sum

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f], instance_expr = Forall(instance_param_or_params = [a], instance_expr = Equals(Sum(index_or_indices = [x], summand = fx, domain = Interval(a, a)), fa), domain = 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())

\forall_{f}~\left[\forall_{a \in \mathbb{Z}}~\left(\left(\sum_{x = a}^{a} f\left(x\right)\right) = f\left(a\right)\right)\right]

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 5
operand: 2
1ExprTuple2
2Lambdaparameter: 24
body: 4
3ExprTuple24
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameter: 32
body: 8
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 26
operands: 13
11Literal
12ExprTuple14, 15
13ExprTuple32, 16
14Operationoperator: 17
operand: 20
15Operationoperator: 24
operand: 32
16Literal
17Literal
18ExprTuple20
19ExprTuple32
20Lambdaparameter: 28
body: 21
21Conditionalvalue: 22
condition: 23
22Operationoperator: 24
operand: 28
23Operationoperator: 26
operands: 27
24Variable
25ExprTuple28
26Literal
27ExprTuple28, 29
28Variable
29Operationoperator: 30
operands: 31
30Literal
31ExprTuple32, 32
32Variable