logo

Expression of type Forall

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, b, l
from proveit.logic import Forall
from proveit.numbers import Exp, Integrate, IntervalCC, LessEq, RealPos, frac, one, two
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = LessEq(Integrate(index_or_indices = [l], integrand = frac(one, Exp(l, two)), domain = IntervalCC(a, b)), frac(one, a)), domain = RealPos, condition = LessEq(a, b))
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_{a, b \in \mathbb{R}^+~|~a \leq b}~\left(\left(\int_{a}^{b} \frac{1}{l^{2}}\,dl\right) \leq \frac{1}{a}\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 37
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 20
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 15
operand: 21
11Operationoperator: 27
operands: 17
12Operationoperator: 29
operands: 18
13Operationoperator: 29
operands: 19
14Operationoperator: 20
operands: 37
15Literal
16ExprTuple21
17ExprTuple31, 40
18ExprTuple40, 22
19ExprTuple41, 22
20Literal
21Lambdaparameter: 38
body: 24
22Literal
23ExprTuple38
24Conditionalvalue: 25
condition: 26
25Operationoperator: 27
operands: 28
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple38, 33
31Literal
32Operationoperator: 34
operands: 35
33Operationoperator: 36
operands: 37
34Literal
35ExprTuple38, 39
36Literal
37ExprTuple40, 41
38Variable
39Literal
40Variable
41Variable