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 Conditional, ExprTuple, Lambda, Omega, Q, Qx, R, Rx, X, f, fx, x
from proveit.logic import Forall, Functions, Implies, InSet
from proveit.numbers import LessEq
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Conditional(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)), 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(f \mapsto \left\{\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) \textrm{ if } f \in \left[X \rightarrow \Omega\right]\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	parameter: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 8
5	Operation	operator: 45 operands: 7
6	ExprTuple	8
7	ExprTuple	38, 9
8	Lambda	parameters: 10 body: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	44, 47
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	49, 16
14	Literal
15	ExprTuple	17, 18
16	Variable
17	Operation	operator: 19 operand: 23
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24, 25
23	Lambda	parameter: 50 body: 26
24	Operation	operator: 28 operand: 30
25	Operation	operator: 28 operand: 31
26	Conditional	value: 43 condition: 34
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Lambda	parameter: 50 body: 32
31	Lambda	parameter: 50 body: 33
32	Conditional	value: 35 condition: 34
33	Conditional	value: 35 condition: 36
34	Operation	operator: 39 operands: 37
35	Operation	operator: 38 operand: 50
36	Operation	operator: 39 operands: 40
37	ExprTuple	42, 41
38	Variable
39	Literal
40	ExprTuple	42, 43
41	Operation	operator: 44 operand: 50
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operand: 50
44	Variable
45	Literal
46	ExprTuple	50, 49
47	Variable
48	ExprTuple	50
49	Variable
50	Variable