Expression of type Equals

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 Omega, x
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Sum, one
from proveit.statistics import Prob, SampleSpaces, prob_domain

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = Prob(x)
expr = Equals(InClass(Omega, SampleSpaces), And(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, prob_domain), domain = Omega), Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Omega), one))).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())

\begin{array}{c} \begin{array}{l} \left(\Omega \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces}\right) =  \\ \left(\left[\forall_{x \in \Omega}~\left(\textrm{Pr}\left(x\right) \in \left[0,1\right]\right)\right] \land \left(\left[\sum_{x \in \Omega}~\textrm{Pr}\left(x\right)\right] = 1\right)\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 13 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	36, 8
6	Literal
7	ExprTuple	9, 10
8	Literal
9	Operation	operator: 11 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 34
15	Lambda	parameter: 35 body: 17
16	Operation	operator: 18 operand: 21
17	Conditional	value: 20 condition: 26
18	Literal
19	ExprTuple	21
20	Operation	operator: 31 operands: 22
21	Lambda	parameter: 35 body: 23
22	ExprTuple	25, 24
23	Conditional	value: 25 condition: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operand: 35
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	35
31	Literal
32	ExprTuple	35, 36
33	Literal
34	Literal
35	Variable
36	Variable