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, R, Rx, X, fx, x
from proveit.logic import Forall, Implies
from proveit.numbers import LessEq
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [Q, R], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Rx, domain = X, condition = Qx), LessEq(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Rx)).with_wrapping_at(2)).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, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X~|~Q\left(x\right)}~R\left(x\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] \leq  \\ \left[\textrm{Prob}_{x \in X~|~R\left(x\right)}~f\left(x\right)\right] \end{array} \end{array}\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: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	34, 37
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameter: 40 body: 16
14	Operation	operator: 18 operand: 20
15	Operation	operator: 18 operand: 21
16	Conditional	value: 33 condition: 24
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 40 body: 22
21	Lambda	parameter: 40 body: 23
22	Conditional	value: 25 condition: 24
23	Conditional	value: 25 condition: 26
24	Operation	operator: 29 operands: 27
25	Operation	operator: 28 operand: 40
26	Operation	operator: 29 operands: 30
27	ExprTuple	32, 31
28	Variable
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operand: 40
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 40
34	Variable
35	Literal
36	ExprTuple	40, 39
37	Variable
38	ExprTuple	40
39	Variable
40	Variable