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, X, f, fx, x
from proveit.logic import Equals, Forall, Functions, SetOfAll
from proveit.statistics import Prob, 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], instance_expr = Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Prob(SetOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx))).with_wrapping_at(2)), domain = 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(X \mapsto \left[\forall_{f \in \left[X \rightarrow \Omega\right]}~\left[\forall_{Q}~\left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \textrm{Pr}\left(\left\{f\left(x\right)~|~Q\left(x\right)\right\}_{x \in X}\right) \end{array} \end{array}\right)\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: 43 body: 3
2	ExprTuple	43
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 34 body: 7
6	ExprTuple	34
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 39 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	34, 14
13	Lambda	parameter: 41 body: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	41
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	43, 21
19	Literal
20	ExprTuple	22, 23
21	Variable
22	Operation	operator: 24 operand: 30
23	Operation	operator: 25 operand: 27
24	Literal
25	Literal
26	ExprTuple	27
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Lambda	parameter: 44 body: 31
31	Conditional	value: 32 condition: 33
32	Operation	operator: 34 operand: 44
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operand: 44
39	Literal
40	ExprTuple	44, 43
41	Variable
42	ExprTuple	44
43	Variable
44	Variable