# from the theory of proveit.statistics¶

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 Omega, X, x
from proveit.logic import Equals, Forall, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob, SampleSpaces

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Omega], instance_expr = Forall(instance_param_or_params = [X], instance_expr = Equals(Prob(X), Sum(index_or_indices = [x], summand = Prob(x), domain = X)), condition = SubsetEq(X, Omega)), domain = SampleSpaces)

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_{\Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}}~\left[\forall_{X~|~X \subseteq \Omega}~\left(\textrm{Pr}\left(X\right) = \left[\sum_{x \in X}~\textrm{Pr}\left(x\right)\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 22
body: 4
3ExprTuple22
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple22, 12
11Lambdaparameter: 35
body: 13
12Literal
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple35, 22
20Operationoperator: 30
operand: 35
21Operationoperator: 24
operand: 26
22Variable
23ExprTuple35
24Literal
25ExprTuple26
26Lambdaparameter: 34
body: 27
27Conditionalvalue: 28
condition: 29
28Operationoperator: 30
operand: 34
29Operationoperator: 32
operands: 33
30Literal
31ExprTuple34
32Literal
33ExprTuple34, 35
34Variable
35Variable