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, X, fx, x
from proveit.logic import Equals, SetOfAll
from proveit.statistics import Prob, ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Prob(SetOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx))).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] =  \\ \textrm{Pr}\left(\left\{f\left(x\right)~|~Q\left(x\right)\right\}_{x \in X}\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: 5 operand: 11
4	Operation	operator: 6 operand: 8
5	Literal
6	Literal
7	ExprTuple	8
8	Operation	operator: 9 operand: 11
9	Literal
10	ExprTuple	11
11	Lambda	parameter: 25 body: 12
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 25
14	Operation	operator: 16 operands: 17
15	Variable
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 25
20	Literal
21	ExprTuple	25, 24
22	Variable
23	ExprTuple	25
24	Variable
25	Variable