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, R, Rx, Ry, X, f, fx, fy, x, y
from proveit.logic import Bijections, Equals, Forall, Implies, 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(X, Forall(instance_param_or_params = [f], instance_expr = 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)), domain = 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(X \mapsto \left[\forall_{f \in \left[X \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]}~\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)\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: 71 body: 3
2	ExprTuple	71
3	Operation	operator: 23 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 62 body: 7
6	ExprTuple	62
7	Conditional	value: 8 condition: 9
8	Operation	operator: 23 operand: 12
9	Operation	operator: 67 operands: 11
10	ExprTuple	12
11	ExprTuple	62, 13
12	Lambda	parameters: 14 body: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	56, 69
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	71, 20
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Operation	operator: 23 operand: 26
22	Operation	operator: 37 operands: 25
23	Literal
24	ExprTuple	26
25	ExprTuple	27, 28
26	Lambda	parameter: 59 body: 29
27	Operation	operator: 49 operand: 34
28	Operation	operator: 31 operands: 32
29	Conditional	value: 33 condition: 52
30	ExprTuple	34
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 37 operands: 38
34	Lambda	parameter: 59 body: 39
35	Literal
36	Operation	operator: 40 operand: 45
37	Literal
38	ExprTuple	53, 42
39	Conditional	value: 43 condition: 44
40	Literal
41	ExprTuple	45
42	Operation	operator: 46 operand: 51
43	Operation	operator: 62 operand: 59
44	Operation	operator: 63 operands: 48
45	Operation	operator: 49 operand: 54
46	Literal
47	ExprTuple	51
48	ExprTuple	52, 53
49	Literal
50	ExprTuple	54
51	Operation	operator: 69 operand: 59
52	Operation	operator: 67 operands: 55
53	Operation	operator: 56 operand: 59
54	Lambda	parameter: 72 body: 58
55	ExprTuple	59, 71
56	Variable
57	ExprTuple	59
58	Conditional	value: 60 condition: 61
59	Variable
60	Operation	operator: 62 operand: 72
61	Operation	operator: 63 operands: 64
62	Variable
63	Literal
64	ExprTuple	65, 66
65	Operation	operator: 67 operands: 68
66	Operation	operator: 69 operand: 72
67	Literal
68	ExprTuple	72, 71
69	Variable
70	ExprTuple	72
71	Variable
72	Variable