Expression of type Neg

from the theory of proveit.statistics

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

# build up the expression from sub-expressions
expr = Neg(ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))

expr:

# 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

# 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]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
notation_in_add	When contained in an Add, use 'subtraction' or 'explicit_negation': For example, 'a - b' versus 'a + (-b)'.	subtraction	subtraction	('with_subtraction_notation', 'without_subtraction_notation')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 20 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 20
9	Operation	operator: 11 operands: 12
10	Variable
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	20, 19
17	Variable
18	ExprTuple	20
19	Variable
20	Variable