logo

Expression of type Neg

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 Ry, X, fy, y
from proveit.numbers import Neg
from proveit.statistics import ProbOfAll
In [2]:
# build up the expression from sub-expressions
expr = Neg(ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))
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())
-\left[\textrm{Prob}_{y \in X~|~R\left(y\right)}~f\left(y\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
notation_in_addWhen contained in an Add, use 'subtraction' or 'explicit_negation': For example, 'a - b' versus 'a + (-b)'.subtractionsubtraction('with_subtraction_notation', 'without_subtraction_notation')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameter: 20
body: 7
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operand: 20
9Operationoperator: 11
operands: 12
10Variable
11Literal
12ExprTuple13, 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operand: 20
15Literal
16ExprTuple20, 19
17Variable
18ExprTuple20
19Variable
20Variable