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 a, b, fx, x
from proveit.logic import Forall, Implies, 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 = Implies(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)\right] \Rightarrow \left(\left(\int_{a}^{b} f\left(x\right)\,dx\right) \in \mathbb{R}\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: 22
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 17
8Lambdaparameter: 24
body: 10
9Operationoperator: 11
operand: 14
10Conditionalvalue: 13
condition: 19
11Literal
12ExprTuple14
13Operationoperator: 22
operands: 15
14Lambdaparameter: 24
body: 16
15ExprTuple18, 17
16Conditionalvalue: 18
condition: 19
17Literal
18Operationoperator: 20
operand: 24
19Operationoperator: 22
operands: 23
20Variable
21ExprTuple24
22Literal
23ExprTuple24, 25
24Variable
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Variable
29Variable