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, fa, fx, x
from proveit.logic import Equals
from proveit.numbers import Interval, Sum

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

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(\sum_{x = a}^{a} f\left(x\right)\right) = f\left(a\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operand: 8
4Operationoperator: 12
operand: 20
5Literal
6ExprTuple8
7ExprTuple20
8Lambdaparameter: 16
body: 9
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operand: 16
11Operationoperator: 14
operands: 15
12Variable
13ExprTuple16
14Literal
15ExprTuple16, 17
16Variable
17Operationoperator: 18
operands: 19
18Literal
19ExprTuple20, 20
20Variable