Expression of type And

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, InSet
from proveit.numbers import Sum, one
from proveit.statistics import Prob, prob_domain

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = Prob(x)
expr = 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))

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 \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)

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.	()	()	('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',)

# display the expression information
stored_expr.expr_info()

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