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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 Omega, X, x
from proveit.logic import Equals, Forall, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob
In [2]:
# build up the expression from sub-expressions
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))
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_{X~|~X \subseteq \Omega}~\left(\textrm{Pr}\left(X\right) = \left[\sum_{x \in X}~\textrm{Pr}\left(x\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 26
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple26, 13
11Operationoperator: 21
operand: 26
12Operationoperator: 15
operand: 17
13Variable
14ExprTuple26
15Literal
16ExprTuple17
17Lambdaparameter: 25
body: 18
18Conditionalvalue: 19
condition: 20
19Operationoperator: 21
operand: 25
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25
23Literal
24ExprTuple25, 26
25Variable
26Variable