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, X, fx, x
from proveit.logic import Equals
from proveit.numbers import Sum
from proveit.statistics import Prob, ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(Q, Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).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(Q \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\textrm{Prob}_{x \in X~|~Q\left(x\right)}~f\left(x\right)\right] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\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	parameter: 28 body: 3
2	ExprTuple	28
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operand: 13
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 31 body: 14
13	Lambda	parameter: 31 body: 15
14	Conditional	value: 22 condition: 17
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operand: 31
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operand: 31
25	Variable
26	Literal
27	ExprTuple	31, 30
28	Variable
29	ExprTuple	31
30	Variable
31	Variable