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, Lambda, 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 = ExprTuple(Lambda([Q, R], 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())

\left(\left(Q, R\right) \mapsto \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)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	33, 36
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameter: 39 body: 15
13	Operation	operator: 17 operand: 19
14	Operation	operator: 17 operand: 20
15	Conditional	value: 32 condition: 23
16	ExprTuple	19
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 39 body: 21
20	Lambda	parameter: 39 body: 22
21	Conditional	value: 24 condition: 23
22	Conditional	value: 24 condition: 25
23	Operation	operator: 28 operands: 26
24	Operation	operator: 27 operand: 39
25	Operation	operator: 28 operands: 29
26	ExprTuple	31, 30
27	Variable
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operand: 39
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operand: 39
33	Variable
34	Literal
35	ExprTuple	39, 38
36	Variable
37	ExprTuple	39
38	Variable
39	Variable