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

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(X, Forall(instance_param_or_params = [f], instance_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)), domain = Functions(X, Omega)).with_wrapping()))

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(X \mapsto \left[\begin{array}{l}\forall_{f \in \left[X \rightarrow \Omega\right]}~\\
\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)\right]\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	parameter: 53 body: 3
2	ExprTuple	53
3	Operation	operator: 23 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 42 body: 7
6	ExprTuple	42
7	Conditional	value: 8 condition: 9
8	Operation	operator: 23 operand: 12
9	Operation	operator: 49 operands: 11
10	ExprTuple	12
11	ExprTuple	42, 13
12	Lambda	parameters: 14 body: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	48, 51
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	53, 20
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Operation	operator: 23 operand: 27
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	Lambda	parameter: 54 body: 30
28	Operation	operator: 32 operand: 34
29	Operation	operator: 32 operand: 35
30	Conditional	value: 47 condition: 38
31	ExprTuple	34
32	Literal
33	ExprTuple	35
34	Lambda	parameter: 54 body: 36
35	Lambda	parameter: 54 body: 37
36	Conditional	value: 39 condition: 38
37	Conditional	value: 39 condition: 40
38	Operation	operator: 43 operands: 41
39	Operation	operator: 42 operand: 54
40	Operation	operator: 43 operands: 44
41	ExprTuple	46, 45
42	Variable
43	Literal
44	ExprTuple	46, 47
45	Operation	operator: 48 operand: 54
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operand: 54
48	Variable
49	Literal
50	ExprTuple	54, 53
51	Variable
52	ExprTuple	54
53	Variable
54	Variable