Expression of type ExprTuple

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 ExprTuple, Qx, Rx, X, fx, x
from proveit.logic import Forall
from proveit.numbers import LessEq
from proveit.statistics import ProbOfAll

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

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_{x \in X~|~Q\left(x\right)}~R\left(x\right), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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