Expression of type Equals

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 Qx, Ry, X, fx, fy, x, y
from proveit.logic import Equals
from proveit.numbers import one, subtract
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
expr = Equals(ProbOfAll(instance_param_or_params = [x], instance_element = fx, domain = X, condition = Qx), subtract(one, ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left(1 - \left[\textrm{Prob}_{y \in X~|~R\left(y\right)}~f\left(y\right)\right]\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 18 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 27 body: 11
9	Literal
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 30 operand: 27
15	Operation	operator: 31 operands: 17
16	Operation	operator: 18 operand: 22
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Operation	operator: 35 operands: 23
21	Operation	operator: 24 operand: 27
22	Lambda	parameter: 40 body: 26
23	ExprTuple	27, 39
24	Variable
25	ExprTuple	27
26	Conditional	value: 28 condition: 29
27	Variable
28	Operation	operator: 30 operand: 40
29	Operation	operator: 31 operands: 32
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operand: 40
35	Literal
36	ExprTuple	40, 39
37	Variable
38	ExprTuple	40
39	Variable
40	Variable