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, R, Rx, Ry, X, fx, fy, x, y
from proveit.logic import 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([Q, R], 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)))

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(\left(Q, R\right) \mapsto \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)

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	parameters: 2 body: 3
2	ExprTuple	41, 54
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 22 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameter: 44 body: 14
12	Operation	operator: 34 operand: 19
13	Operation	operator: 16 operands: 17
14	Conditional	value: 18 condition: 37
15	ExprTuple	19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Lambda	parameter: 44 body: 24
20	Literal
21	Operation	operator: 25 operand: 30
22	Literal
23	ExprTuple	38, 27
24	Conditional	value: 28 condition: 29
25	Literal
26	ExprTuple	30
27	Operation	operator: 31 operand: 36
28	Operation	operator: 47 operand: 44
29	Operation	operator: 48 operands: 33
30	Operation	operator: 34 operand: 39
31	Literal
32	ExprTuple	36
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	39
36	Operation	operator: 54 operand: 44
37	Operation	operator: 52 operands: 40
38	Operation	operator: 41 operand: 44
39	Lambda	parameter: 57 body: 43
40	ExprTuple	44, 56
41	Variable
42	ExprTuple	44
43	Conditional	value: 45 condition: 46
44	Variable
45	Operation	operator: 47 operand: 57
46	Operation	operator: 48 operands: 49
47	Variable
48	Literal
49	ExprTuple	50, 51
50	Operation	operator: 52 operands: 53
51	Operation	operator: 54 operand: 57
52	Literal
53	ExprTuple	57, 56
54	Variable
55	ExprTuple	57
56	Variable
57	Variable