# from the theory of proveit.numbers.integration¶

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 ExprTuple, a, b, fx, x
from proveit.logic import Forall, InSet
from proveit.numbers import Integrate, IntervalCC, Real

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = IntervalCC(a, b)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(fx, Real), domain = sub_expr2), InSet(Integrate(index_or_indices = sub_expr1, integrand = fx, domain = sub_expr2), Real))

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(\forall_{x \in \left[a,b\right]}~\left(f\left(x\right) \in \mathbb{R}\right), \left(\int_{a}^{b} f\left(x\right)\,dx\right) \in \mathbb{R}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 3
operand: 6
2Operationoperator: 20
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 15
6Lambdaparameter: 22
body: 8
7Operationoperator: 9
operand: 12
8Conditionalvalue: 11
condition: 17
9Literal
10ExprTuple12
11Operationoperator: 20
operands: 13
12Lambdaparameter: 22
body: 14
13ExprTuple16, 15
14Conditionalvalue: 16
condition: 17
15Literal
16Operationoperator: 18
operand: 22
17Operationoperator: 20
operands: 21
18Variable
19ExprTuple22
20Literal
21ExprTuple22, 23
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Variable
27Variable