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Expression of type Forall

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Q, Qx, X, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Sum
from proveit.statistics import Prob, ProbOfAll
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [Q], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2))
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_{Q}~\left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\right] \end{array} \end{array}\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
3Lambdaparameter: 30
body: 5
4ExprTuple30
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operand: 15
10Literal
11ExprTuple14
12Literal
13ExprTuple15
14Lambdaparameter: 33
body: 16
15Lambdaparameter: 33
body: 17
16Conditionalvalue: 24
condition: 19
17Conditionalvalue: 18
condition: 19
18Operationoperator: 20
operand: 24
19Operationoperator: 22
operands: 23
20Literal
21ExprTuple24
22Literal
23ExprTuple25, 26
24Operationoperator: 27
operand: 33
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operand: 33
27Variable
28Literal
29ExprTuple33, 32
30Variable
31ExprTuple33
32Variable
33Variable