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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
from proveit.logic import Equals, Forall
from proveit.numbers import Sum, one
from proveit.statistics import Prob, SampleSpaces
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Omega], instance_expr = Equals(Sum(index_or_indices = [x], summand = Prob(x), domain = Omega), one), 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(\left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1\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: 5
4ExprTuple26
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple26, 14
12Operationoperator: 15
operand: 17
13Literal
14Literal
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