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, Injections
from proveit.numbers import Sum
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), Sum(index_or_indices = sub_expr1, summand = Prob(fx), domain = X, condition = Qx)).with_wrapping_at(2)), domain = Injections(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 \xrightarrow[]{\text{1-to-1}} \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] =  \\ \left[\sum_{x \in X~|~Q\left(x\right)}~\textrm{Pr}\left(f\left(x\right)\right)\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: 46 body: 3
2	ExprTuple	46
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 41 body: 7
6	ExprTuple	41
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 42 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	41, 14
13	Lambda	parameter: 44 body: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	44
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	46, 21
19	Literal
20	ExprTuple	22, 23
21	Variable
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Lambda	parameter: 47 body: 30
29	Lambda	parameter: 47 body: 31
30	Conditional	value: 38 condition: 33
31	Conditional	value: 32 condition: 33
32	Operation	operator: 34 operand: 38
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38
36	Literal
37	ExprTuple	39, 40
38	Operation	operator: 41 operand: 47
39	Operation	operator: 42 operands: 43
40	Operation	operator: 44 operand: 47
41	Variable
42	Literal
43	ExprTuple	47, 46
44	Variable
45	ExprTuple	47
46	Variable
47	Variable