Expression of type Forall

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

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = 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))

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# 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	Lambda	parameter: 27 body: 5
4	ExprTuple	27
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operand: 16
9	Operation	operator: 11 operand: 13
10	Literal
11	Literal
12	ExprTuple	13
13	Operation	operator: 14 operand: 16
14	Literal
15	ExprTuple	16
16	Lambda	parameter: 30 body: 17
17	Conditional	value: 18 condition: 19
18	Operation	operator: 20 operand: 30
19	Operation	operator: 21 operands: 22
20	Variable
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operand: 30
25	Literal
26	ExprTuple	30, 29
27	Variable
28	ExprTuple	30
29	Variable
30	Variable