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, R, Rx, Ry, X, f, fx, fy, x, y
from proveit.logic import Bijections, Equals, Forall, Implies, InSet, Not
from proveit.numbers import one, subtract
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Conditional(Forall(instance_param_or_params = [Q, R], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qx, Not(Rx)), domain = X), Equals(ProbOfAll(instance_param_or_params = sub_expr1, instance_element = fx, domain = X, condition = Qx), subtract(one, ProbOfAll(instance_param_or_params = [y], instance_element = fy, domain = X, condition = Ry))).with_wrapping_at(2)).with_wrapping_at(2)), InSet(f, Bijections(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, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x \in X}~\left(Q\left(x\right) = (\lnot R\left(x\right))\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] =  \\ \left(1 - \left[\textrm{Prob}_{y \in X~|~R\left(y\right)}~f\left(y\right)\right]\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } f \in \left[X \xrightarrow[\text{onto}]{\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: 58 body: 3
2	ExprTuple	58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 8
5	Operation	operator: 63 operands: 7
6	ExprTuple	8
7	ExprTuple	58, 9
8	Lambda	parameters: 10 body: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	52, 65
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	67, 16
14	Literal
15	ExprTuple	17, 18
16	Variable
17	Operation	operator: 19 operand: 22
18	Operation	operator: 33 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	23, 24
22	Lambda	parameter: 55 body: 25
23	Operation	operator: 45 operand: 30
24	Operation	operator: 27 operands: 28
25	Conditional	value: 29 condition: 48
26	ExprTuple	30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 33 operands: 34
30	Lambda	parameter: 55 body: 35
31	Literal
32	Operation	operator: 36 operand: 41
33	Literal
34	ExprTuple	49, 38
35	Conditional	value: 39 condition: 40
36	Literal
37	ExprTuple	41
38	Operation	operator: 42 operand: 47
39	Operation	operator: 58 operand: 55
40	Operation	operator: 59 operands: 44
41	Operation	operator: 45 operand: 50
42	Literal
43	ExprTuple	47
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	50
47	Operation	operator: 65 operand: 55
48	Operation	operator: 63 operands: 51
49	Operation	operator: 52 operand: 55
50	Lambda	parameter: 68 body: 54
51	ExprTuple	55, 67
52	Variable
53	ExprTuple	55
54	Conditional	value: 56 condition: 57
55	Variable
56	Operation	operator: 58 operand: 68
57	Operation	operator: 59 operands: 60
58	Variable
59	Literal
60	ExprTuple	61, 62
61	Operation	operator: 63 operands: 64
62	Operation	operator: 65 operand: 68
63	Literal
64	ExprTuple	68, 67
65	Variable
66	ExprTuple	68
67	Variable
68	Variable