Expression of type Conditional

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 Conditional, Omega, Q, Qx, X, f, fx, x
from proveit.logic import Equals, Forall, Functions, InSet, SetOfAll
from proveit.statistics import Prob, ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [Q], instance_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)), InSet(f, Functions(X, Omega)))

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\{\forall_{Q}~\left(\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}\right) \textrm{ if } f \in \left[X \rightarrow \Omega\right]\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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