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, Qx, Rx, Ry, X, fx, fy, x, y
from proveit.logic import Equals, Forall, Not
from proveit.numbers import one, subtract
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(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))

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(\forall_{x \in X}~\left(Q\left(x\right) = (\lnot R\left(x\right))\right), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 39 body: 9
7	Operation	operator: 29 operand: 14
8	Operation	operator: 11 operands: 12
9	Conditional	value: 13 condition: 32
10	ExprTuple	14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operands: 18
14	Lambda	parameter: 39 body: 19
15	Literal
16	Operation	operator: 20 operand: 25
17	Literal
18	ExprTuple	33, 22
19	Conditional	value: 23 condition: 24
20	Literal
21	ExprTuple	25
22	Operation	operator: 26 operand: 31
23	Operation	operator: 42 operand: 39
24	Operation	operator: 43 operands: 28
25	Operation	operator: 29 operand: 34
26	Literal
27	ExprTuple	31
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	34
31	Operation	operator: 49 operand: 39
32	Operation	operator: 47 operands: 35
33	Operation	operator: 36 operand: 39
34	Lambda	parameter: 52 body: 38
35	ExprTuple	39, 51
36	Variable
37	ExprTuple	39
38	Conditional	value: 40 condition: 41
39	Variable
40	Operation	operator: 42 operand: 52
41	Operation	operator: 43 operands: 44
42	Variable
43	Literal
44	ExprTuple	45, 46
45	Operation	operator: 47 operands: 48
46	Operation	operator: 49 operand: 52
47	Literal
48	ExprTuple	52, 51
49	Variable
50	ExprTuple	52
51	Variable
52	Variable