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, X, f, fx, x
from proveit.logic import Equals, Forall, InSet, 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(f, Conditional(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)), InSet(f, 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(f \mapsto \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) \textrm{ if } f \in \left[X \xrightarrow[]{\text{1-to-1}} \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: 37 body: 3
2	ExprTuple	37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 38 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	37, 10
9	Lambda	parameter: 40 body: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	40
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	42, 17
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Operation	operator: 20 operand: 24
19	Operation	operator: 22 operand: 25
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	Lambda	parameter: 43 body: 26
25	Lambda	parameter: 43 body: 27
26	Conditional	value: 34 condition: 29
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operand: 34
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	35, 36
34	Operation	operator: 37 operand: 43
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operand: 43
37	Variable
38	Literal
39	ExprTuple	43, 42
40	Variable
41	ExprTuple	43
42	Variable
43	Variable